A study is going to be conducted in which a mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval. The estimate needs to be within +/- 2 hours of the actual population mean. The population standard deviation s is estimated to be around 25. The necessary sample size should be at least _______.

Answer:

what grade are you in so then I could get the answer

Answer:

[tex] |78| + |12| = |12| + |78| [/tex]

Answer: a) 84 and b ) 2084

Step-by-step explanation:

Given : Sample standard deviation : s= $22.82

(Population standard deviation is unknown ) , so we use t-test.

Critical value or the​ 95% confidence intervals :[tex]t_{n-1}*=2.0[/tex]

Formula to find the sample size :

[tex]n=(\dfrac{t^*\cdot s}{E})^2[/tex]

a) E = 5

[tex]n=(\dfrac{(2)\cdot 22.82}{5})^2[/tex]

[tex]n=(9.128)^2=83.320384\approx84[/tex]

i.e. Required sample size : n= 84

b)  E = 1

[tex]n=(\dfrac{(2)\cdot 22.82}{1})^2[/tex]

[tex]n=(45.64)^2=2083.0096\approx2084[/tex]

i.e. Required sample size : n= 2084

Answer:

There is an 8.22% probability that a randomly selected person has a birthday in November.

Step-by-step explanation:

The theoretical method to find the probability is the division of the number of desired outcomes by the number of total outcomes.

A randomly selected person has a birthday in November

There are 365 days in a year, so the number of total outcomes is 365.

There are 30 days in november, so the number of desired outcomes is 30.

So the probability is

[tex]P = \frac{30}{365} = 0.0822[/tex]

There is an 8.22% probability that a randomly selected person has a birthday in November.

Answer:

The probability of a randomly selected person has a birthday in November is [tex]8.2\%[/tex]

Explanation

A randomly selected person has a birthday in November

The probability of the event is

[tex]$P(B)=\frac{\text { No }of \text { days in november }}{No\ of \text { days in year }}$[/tex]

[tex]$P(B)=\frac{30}{365}$[/tex]

[tex]P(B)=8.2\%[/tex]

Therefore, the probability of a randomly selected person has a birthday in November is [tex]8.2\%[/tex]

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Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

[tex]1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}[/tex]

Now, differentiate to obtain

[tex]\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}[/tex]

[tex]=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}[/tex]

To obtain the required form, extract a factor in both the numerator and denominator:

[tex]\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)[/tex]

Answer:

$48.72

Step-by-step explanation:

Step 1: identify the given parameters

Sky's gross annual income = $36,192

Step 2: calculate Sky's weekly salary

= 36,192/52

=$696/week

Step 3: calculate Sky's weekly 4% deduction

= $696 X 4%

=$696 X 0.04 = $27.84

Step 4: calculate Sky's weekly 3% deduction

= $696 X 3%

=$696 X 0.03 = $20.88

Step 5: calculate how much is deposited into Skye’s 403(b) each payday

= $27.84 + $20.88

=$48.72

Answer: 48.72

Step-by-step explanation:

To test the minister's claim, the correct null and alternative hypotheses would be H0 : p = .6 and Ha: p > .6, which aligns with the suggestion that more than 60% of the population attends religious services. These hypotheses represent equality and inequality respectively, and are tested to determine if there is sufficient statistical evidence for the claim.

To test the minister's claim, Letter b is the correct choice. The notation 'p' is typically used to denote a proportion in a population. The null hypothesis, denoted H0, would be that the proportion of the population who attend services (p) is equal to 0.6. The alternative hypothesis, denoted Ha, would state that the proportion of the population who attend services (p) is greater than 0.6 which aligns with the minister's claim.

Therefore:
H0 : p = .6
Ha: p > .6

This is because the minister’s claim is a statement of inequality (more than 60%), so the alternative hypothesis must reflect this particular inequality. We then test the null hypothesis to determine whether there is enough statistical evidence to accept the alternative hypothesis.

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Final answer:

Option b is the correct answer; H0: p = 0.6 and Ha: p > 0.6. These hypotheses are set for a right-tailed test to assess the claim that more than 60% of adults attend religious services monthly.

Explanation:

The correct answer to the question of which null and alternative hypotheses should be used to test the minister's claim that more than 60% of the adult population attends a religious service at least once a month is option b. The null hypothesis (H0) signifies the statement that is presumed true before the data evidence is considered, while the alternative hypothesis (Ha) represents the claim to be tested. In this case, the null hypothesis should state that the population proportion (p) equals 0.6, or H0: p = 0.6, indicating that 60% of the adult population attends a religious service at least once a month.

The alternative hypothesis should indicate that the proportion is greater than 0.6, or Ha: p > 0.6, which aligns with the minister's claim and sets up the hypothesis test for a right-tailed test. The other options are incorrect as they either test for a mean instead of a proportion, use the wrong symbol for the hypotheses, or present the hypothesis in an incorrect format.

Answer:

1)  n=48  

2) n=298

3) n=426

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]p[/tex] represent the real population proportion of interest

[tex]\hat p[/tex] represent the estimated proportion for the sample

n is the sample size required (variable of interest)

[tex]z[/tex] represent the critical value for the margin of error

The population proportion have the following distribution  

[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]  

Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.10[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:  

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]  

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)  

And on this case we have that [tex]ME =\pm 0.1[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:  

[tex]n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63[/tex]  

And rounded up we have that n=48  

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

[tex]n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7[/tex]  

And rounded up we have that n=298  

Part 3

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:  

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]  

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)  

And on this case we have that [tex]ME =\pm 0.04[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:  

[tex]n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.96})^2}=425.22[/tex]  

And rounded up we have that n=426  

The probability shows that the number of younger age group that must will be surveyed will be 48.

From the information given, the confidence level is 90%, margin or error is 0.1. The critical value from the z table is given as 1.645.

The number of samples will be:

= 0.23 × (1 - 0.23) × (1.645/0.1)²

= 0.23 × 0.77 × (1.645/0.1)²

= 48

The sample size when we are 90% confidence but we want to cut the margin of error to .04 will be computed thus:

= (1.645/.004)² × 0.23 × (1 - 0.23)

= (41.125)² × 0.1771

= 300

The sample size that is needed to estimate the proportion of non-grads to within .04 with 95% confidence will be:

= (1.96/0.04)² × 0.23 × (1 - 0.23)

= 48.99 × 0.1771

= 426

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Answer:

option C

Step-by-step explanation:

given,

[tex]\bar{x_1} = 158.706, \sigma_1 = 25.36 , n_1= 17[/tex]

[tex]\bar{x_1} = 122.471, \sigma_1 = 25.183 , n_2= 17[/tex]

α = 1 - 0.95 = 0.05

degree of freedom (df) = 17 -1 = 16

critical value[tex]= t_{\alpha/2},df = t_{0.025},16 =2.120[/tex] (from t-table)

margin of error = [tex]t_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}[/tex]

=2.120\times \sqrt{\dfrac{25.36^2}{17}+\dfrac{25.183^2}{17}}[/tex]

= 2.120 x 8.6467

= 18.33

Margin of error = 18.33

Point estimation of difference = [tex]\bar{x_1} - \bar{x_2}[/tex]

                                                  = 36.235

lower limit = 36.235 - 18.33 = 17.91

upper limit = 36.235 + 18.33 = 54.57

hence, the nearest option near to answer is option C

Answer:

[tex]P(X\leq -1.5) = P(X < -1.5)=P(Z<-1.5)=0.067[/tex]

Step-by-step explanation:

For this case we know that our random variable X="weight loss or gain" is distributed on this way:

[tex]X \sim N (\mu =0, \sigma=1)[/tex]

And we want the probability a person loses 1.5 pounds or more. If we interpret this an individual person losses 1.5 pounds or more if our random variable is equal or lower than 1.5. That means this:

[tex]P(X\leq -1.5) = P(X < -1.5)=P(Z<-1.5)[/tex]

And for this case we can use the normal standard distribution or excel with the following code:

"=NORM.DIST(-1.5,0,1,TRUE)"

And we got:

[tex]P(X\leq -1.5) = P(X < -1.5)=P(Z<-1.5)=0.067[/tex]

We need to remember that if the negative number decrease on the weight loss we are increasing the loss. For this reason we just need to find P(X<-1.5).

Answer:

[tex]z=\frac{0.28 -0.34}{\sqrt{\frac{0.34(1-0.34)}{116}}}=-1.364[/tex]  

[tex]p_v =2*P(Z<-1.364)=0.173[/tex]  

The p value obtained was a very high value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIl to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduates from the previous year claim to have encountered unethical business practices in the workplace is not significant different from 0.34.  

Step-by-step explanation:

1) Data given and notation

n=116 represent the random sample taken

X represent the number graduates from the previous year claim to have encountered unethical business practices in the workplace

[tex]\hat p=0.28[/tex] estimated proportion of graduates from the previous year claim to have encountered unethical business practices in the workplace

[tex]p_o=0.34[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is 0.34 or no.:  

Null hypothesis:[tex]p=0.34[/tex]  

Alternative hypothesis:[tex]p \neq 0.34[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.28 -0.34}{\sqrt{\frac{0.34(1-0.34)}{116}}}=-1.364[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(Z<-1.364)=0.173[/tex]  

The p value obtained was a very high value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIl to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduates from the previous year claim to have encountered unethical business practices in the workplace is not significant different from 0.34.  

Answer:

Mean = 3.8, std dev = 3.06

Step-by-step explanation:

First let us select any 5 integers without repitition from 0 to 10

Let this be 0,2,3,5,9

To calculate mean and standard deviation

x (x-3.8)^2  

0 14.44  

2 3.24  

3 0.64  

5 1.44  

9 27.04  

total 19 46.8  

Mean 3.8 9.36 Variance

Variance 9.36  

Std dev 3.059411708  

Please note that this mean and std deviation would vary according to our selection of 5 integers.

The standard deviation of the set {2, 4, 6, 8, 10} is approximately 2.83.

To calculate the standard deviation of a set of 5 different integers, each of which is between 0 and 10, you'll first need to find the mean (average) of the set and then calculate the squared differences from the mean. Here are the steps:

Find the mean (average) of the set:

Add up all the integers and divide by the number of integers (in this case, 5).

Calculate the squared differences from the mean:

For each integer in the set, subtract the mean and then square the result. Do this for all 5 integers.

Find the variance:

Add up all the squared differences from step 2 and divide by the number of integers (5 in this case).

Calculate the standard deviation:

Take the square root of the variance to find the standard deviation.

Let's go through an example:

Suppose you have the following set of 5 different integers between 0 and 10: {2, 4, 6, 8, 10}

Find the mean:

(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6

Calculate the squared differences from the mean:

(2 - 6)^2 = 16

(4 - 6)^2 = 4

(6 - 6)^2 = 0

(8 - 6)^2 = 4

(10 - 6)^2 = 16

Find the variance:

(16 + 4 + 0 + 4 + 16) / 5 = 40 / 5 = 8

Calculate the standard deviation:

√8 ≈ 2.83 (rounded to two decimal places)

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Answer:

108 rooms

Step-by-step explanation:

Robin can clean 72 rooms in 666 days

means in 666 days rooms that can be clean  is 72 rooms

in 1 days rooms that can be clean  is 72/666 rooms

in 999 days rooms can be clean is  999\times 72\div 666

after solving we get 108 answer

Answer:

[tex]z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124[/tex]  

Null hypothesis:[tex]p\geq 0.8[/tex]  

Alternative hypothesis:[tex]p < 0.8[/tex]  

Since is a left tailed test the p value would be:  

[tex]p_v =P(Z<2.124)=0.983[/tex]  

So the p value obtained was a very high value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis:[tex]p\leq 0.8[/tex]  

Alternative hypothesis:[tex]p > 0.8[/tex]

[tex]p_v =P(Z>2.124)=0.013[/tex]  

So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation  

n=110 represent the random sample taken

X=97 represent the students who completed the modules before class

[tex]\hat p=\frac{97}{110}=0.882[/tex] estimated proportion of students who completed the modules before class

[tex]p_o=0.8[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v{/tex} represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.8 or 80%:  

Null hypothesis:[tex]p\geq 0.8[/tex]  

Alternative hypothesis:[tex]p < 0.8[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

[tex]p_v =P(Z<2.124)=0.983[/tex]  

So the p value obtained was a very high value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis:[tex]p\leq 0.8[/tex]  

Alternative hypothesis:[tex]p > 0.8[/tex]

[tex]p_v =P(Z>2.124)=0.013[/tex]  

So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis.

Based on the given data, we do not reject the null hypothesis because the p-value (0.1308) is greater than the alpha level (0.05). Therefore, we conclude that there is insufficient evidence to suggest that fewer than 80% of ST 311 Hybrid students complete all modules before class.

To determine whether fewer than 80% of ST 311 Hybrid students complete all modules before class, we conducted a hypothesis test with the following hypotheses:

We collected data from a sample of 110 students, where 97 had completed the modules before class. The test resulted in a p-value of 0.1308.

Conclusion: There is insufficient evidence to conclude that fewer than 80% of the students complete all modules before class.

Answer:

[tex]x(x+1)^2[/tex]

Step-by-step explanation:

Given:

The expression to factor is given as:

[tex]x^3+2x^2+x[/tex]

In order to factor it, we write the factors of each of the terms of the given polynomial. So,

The factors of the three terms are:

[tex]x^3=x\times x\times x\\\\2x^2=2\times x\times x\\\\x=x[/tex]

Now, 'x' is a common factor for all the three terms. So, we factor it out. This gives,

[tex]x(\frac{x^3}{x}+2\frac{x^2}{x}+\frac{x}{x})\\\\x(x^2+2x+1)[/tex]

Now, we know a identity which is given as:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Here, [tex]x^2+2x+1[/tex] can be rewritten as [tex]x^2+2(1)(x)+1^2[/tex]

So, [tex]a=x\ and\ b=1[/tex]

Thus, [tex]x^2+2(1)(x)+1^2= (x+1)^2[/tex]

Therefore, the complete factorization of the given expression is:

[tex]x^3+2x^2+x=x(x+1)^2[/tex]

Answer:

x(x+1)^2

Step-by-step explanation:

Answer:

[tex]t=\frac{(950 -915)-(0)}{\sqrt{\frac{50^2}{30}}+\frac{45^2}{25}}=2.73[/tex]  

[tex]p_v =2*P(t_{53}>2.73) =0.0086[/tex]  

So with the p value obtained and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Philadelphia) is  significantly different than the mean for the group 2 (Baltimore).  

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]  

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]  

Or equivalently:  

Null hypothesis: [tex]\mu_1 - \mu_2 = 0[/tex]  

Alternative hypothesis: [tex]\mu_1 -\mu_2\neq 0[/tex]  

Our notation on this case :  

[tex]n_1 =30[/tex] represent the sample size for group 1  (Philadelphia)

[tex]n_2 =25[/tex] represent the sample size for group 2  (Baltimore)

[tex]\bar X_1 =950[/tex] represent the sample mean for the group 1  

[tex]\bar X_2 =915[/tex] represent the sample mean for the group 2  

[tex]s_1=50[/tex] represent the sample standard deviation for group 1  

[tex]s_2=45[/tex] represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test or two tail.

Critical values

On this case since the significance level is 0.05 and we are conducting a bilateral test we have two critical values, and we need on each tail of the distribution [tex]\alpha/2 = 0.025[/tex] of the area.  

The distribution on this case since we don't know the population deviation for both samples is the t distribution with [tex]df=n_1+n_2 -2= 30+25-2=53[/tex] degrees of freedom.

We can use the following excel codes in order to find the critical values:

"=T.INV(0.025,53)", "=T.INV(1-0.025,53)"

And we got: (-2.01, 2.01)

Calculate th statistic

The statistic is given by this formula:  

[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}[/tex]  

And now we can calculate the statistic:  

[tex]t=\frac{(950 -915)-(0)}{\sqrt{\frac{50^2}{30}}+\frac{45^2}{25}}=2.73[/tex]  

The degrees of freedom are given by:  

[tex]df=30+25-2=53[/tex]

P value

And now we can calculate the p value using the altenative hypothesis:  

[tex]p_v =2*P(t_{53}>2.73) =0.0086[/tex]  

So with the p value obtained and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (Philadelphia) is  significantly different than the mean for the group 2 (Baltimore).  

Area of Jhons planter is 164.89 square inches

Solution:

Given that,

Jhons garden has a big planter that measures [tex]18\frac{2}{3}[/tex] in by [tex]8 \frac{5}{6}[/tex] inches

To find: area of Jhons planter

From given information,

[tex]\text{ length } = 18\frac{2}{3} = \frac{3 \times 18 + 2}{3} = \frac{56}{3} \text{ inches }[/tex]

[tex]\text{ width } = 8\frac{5}{6} = \frac{6 \times 8 + 5}{6} = \frac{53}{6} \text{ inches }[/tex]

The area of planter is given as:

[tex]area = length \times width[/tex]

[tex]area = \frac{56}{3} \times \frac{53}{6} = \frac{2968}{18} = 164.89[/tex]

Thus area of Jhons planter is 164.89 square inches

Answer:

[tex]f(4) = 1501 + 9e^{-2*4} = 1501.00[/tex]

Step-by-step explanation:

f(4) is the value of f when x = 4.

We have that

[tex]f(x) = 1501 + 9e^{-2x}[/tex]

So

[tex]f(4) = 1501 + 9e^{-2*4} = 1501.00[/tex]

Answer:1501

Step-by-step explanation:

The given logistic model is expressed as

f(x)=1501+9e−2x

To evaluate the function at f(4), we would substitute x = 4 into the given logistic model. It becomes

f(4)=1501+9e−2 × 4

f(4)=1501+9e−8

Input 1501 plus 9 plus shift Ln plus -8 in a calculator. It becomes

1501 + 0.00302 = 1501.00302

Approximating to the nearest tenth, it becomes I501

Answer:

a) [tex]k = 0.000124[/tex]

b) According to these data, the Shroud of Turin has around 760 years.

Step-by-step explanation:

The amount of carbon-14 is modeled by the following equation:

[tex]C(t) = C_{0}e^{-kt}[/tex]

In which [tex]C_{0}[/tex] is the initial amount and k is the rate of decrease.

(a) Find the value of the constant k in the differential equation.

Half-life of 5595 years.

So [tex]C(5595) = 0.5C_{0}[/tex]

[tex]C(t) = C_{0}e^{-kt}[/tex]

[tex]0.5C_{0} = C_{0}e^{-5595k}[/tex]

[tex]e^{-5595k} = 0.5[/tex]

Applying ln to both sides

[tex]-5595k = -0.69[/tex]

[tex]k = 0.000124[/tex]

b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material. How old is the Shroud of Turin, according to these data?

This is t when [tex]C(t) = 0.91C_{0}[/tex]

[tex]C(t) = C_{0}e^{-kt}[/tex]

[tex]0.91C_{0} = C_{0}e^{-0.000124t}[/tex]

[tex]e^{-0.000124t} = 0.91[/tex]

Applying ln to both sides

[tex]-0.000124t = -0.094[/tex]

[tex]t = 760.57[/tex]

According to these data, the Shroud of Turin has around 760 years.

Answer:

Null hypothesis:[tex]\mu_{m} \geq \mu_{w}[/tex]

Alternative hypothesis:[tex]\mu_{m} < \mu_{w}[/tex]

[tex]p_v =P(t_{134}<-2.85)=0.0025[/tex]

D. Reject H0, there is sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women.

So on this case the 95% confidence interval would be given by [tex]-10.502 \leq \mu_{m} -\mu_w \leq -1.898[/tex]  

We are 95% confident that the mean difference is in the confidence interval.

Step-by-step explanation:

1) Data given and notation

[tex]\bar X_{m}=112.5[/tex] represent the mean for the sample of men

[tex]\bar X_{w}=118.7[/tex] represent the mean for the sample women

[tex]s_{m}=11.1[/tex] represent the sample standard deviation for the sample men

[tex]s_{w}=14.2[/tex] represent the sample standard deviation for the sample eomen

[tex]n_{m}=56[/tex] sample size for the group men

[tex]n_{w}=80[/tex] sample size for the group women

z would represent the statistic (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{m} \geq \mu_{w}[/tex]

Alternative hypothesis:[tex]\mu_{m} < \mu_{w}[/tex]

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{m}-\bar X_{w}}{\sqrt{\frac{s^2_{m}}{n_{m}}+\frac{s^2_{w}}{n_{w}}}}[/tex] (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

With the info given we can replace in formula (1) like this:

[tex]t=\frac{112.5-118.7}{\sqrt{\frac{11.1^2}{56}+\frac{14.2^2}{80}}}}=-2.85[/tex]  

4) Statistical decision

The degrees of freedom are given by:

[tex]df=n_m +n_w -2= 56+80-2=134[/tex]

Since is a left tailed test the p value would be:

[tex]p_v =P(t_{134}<-2.85)=0.0025[/tex]

D. Reject H0, there is sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women.

5) Confidence interval

The confidence interval for the difference of means is given by the following formula:  

[tex](\bar X_m -\bar X_w) \pm t_{\alpha/2}\sqrt{(\frac{s^2_m}{n_m}+\frac{s^2_w}{n_w})}[/tex] (1)  

The point of estimate for [tex]\mu_1 -\mu_2[/tex] is just given by:  

[tex]\bar X_m -\bar X_w =112.5-118.7=-6.2[/tex]  

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,134)".And we see that [tex]z_{\alpha/2}=1.98[/tex]  

Now we have everything in order to replace into formula (1):  

[tex]-6.2-1.98\sqrt{\frac{11.1^2}{56}+\frac{14.2^2}{80}}}=-10.502[/tex]  

[tex]-6.2+1.98\sqrt{\frac{11.1^2}{56}+\frac{14.2^2}{80}}}=-1.898[/tex]  

So on this case the 95% confidence interval would be given by [tex]-10.502 \leq \mu_{m} -\mu_w \leq -1.898[/tex]  

We are 95% confident that the mean difference is in the confidence interval.

In the context of the study conducted by the physical therapist, the null hypothesis states that the mean step pulse of men equals the mean step pulse of women, and the alternative hypothesis states that the mean step pulse of men is less than that of women. With a t-test result that has a P-value less than 0.05, we reject the null hypothesis and accept the alternative hypothesis, indicating a significant difference between the mean step pulses of men and women.

The physical therapist's study is essentially a hypothesis testing problem. The null hypothesis (σ_0) is that the mean step pulse of men is equal to the mean step pulse of women, and the alternative hypothesis (σ_a) is that the mean step pulse of men is less than the mean step pulse of women.

For this problem, we can write the hypotheses as follows:
σ_0: μ1 = μ2
σ_a: μ1 < μ2

The student's available choices seem to reflect this. Choosing between 'H0: μ1 = μ2; Ha :μ1>μ2' and 'H0:μ1 = μ2;Ha::μ1 not equal μ2'. The correct choice is not listed because the alternative hypothesis is incorrectly defined in both cases. The correct alternative hypothesis would be 'μ1 < μ2', pointing that the mean step pulse of men is less than that of women.

The t-test result given in the question 'T = 2.85 P = 0.0025 DF = 132' indicates that the mean step pulse of men is not equal to that of women, with the P-value being less than 0.05. Thus, with this information, you would typically reject the null hypothesis and accept the alternative hypothesis, which suggests a significant difference between the mean step pulses of men and women.

https://brainly.com/question/34171008

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Answer:

a) i) This is a right-tailed test.

b)

[tex]\text{Test statistic} = 1.08[/tex]

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 23 pounds

Sample mean, [tex]\bar{x}[/tex] = 23.6 pounds

Sample size, n = 40

Alpha, α = 0.10

Sample standard deviation, s = 3.5 pounds

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 23\text{ pounds}\\H_A: \mu > 23\text{ pounds}[/tex]

This is a one tailed(right).

Formula:

[tex]\text{Test statistic} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]\text{Test statistic} = \displaystyle\frac{23.6 - 23}{\frac{3.5}{\sqrt{40}} } = 1.08[/tex]

Answer:   c. should be rejected  

Step-by-step explanation:

n = 14

s = 20

H0: σ2 ≤ 500 and Ha: σ2 > 500

Answer:

This information indicates that the mean level of arsenic in this well is less than 8 ppbat  0.01 level of signifcance..

Step-by-step explanation:

Given that a well in Texas is used to water crops.

This well is tested on a regular basis for arsenic.

A random sample of 36 tests gave a sample mean of = 7.3 ppb arsenic, with s = 1.9 ppb

H0: Sample mean = 8

Ha: Sample mean <8

(left tailed test at 1% level)

Mean difference =-0.70

Std error of mean = [tex]\frac{1.9}{\sqrt{36} } \\=0.3167[/tex]

Test statistic t = -2.204

df = 35

p value = 0.0171

Since p >0.01 we accept H0

This information indicates that the mean level of arsenic in this well is less than 8 ppbat  0.01 level of signifcance..

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

m = slope

The equation of the given line is

y = - 23x+5

Comparing it with the slope intercept equation, slope, m = -23

If a line is perpendicular to another line, the slope of the line is the negative reciprocal of the given line. This means that the slope of the line passing through the point (8, 1) is 1/23

We would determine the intercept, c by substituting m = 1/23, x = 8 and y = 1 into y = mx + c. It becomes

1 = 1/23 × 8 + c

1 = 8/23 + c

c = 1 - 8/23 = 15/23

The equation becomes

y = x/23 + 15/23

Answer:

619.13 feet

Step-by-step explanation:

Please find the attachment.

Let x represent the distance between doghouse to the foot of the tower.

We have been given that from the top of a vertical tower, 331 feet above the surface of the earth, the angle of depression to a doghouse is 28 degrees 8'. We are asked to find the distance between doghouse to the foot of the tower.

First of all, we will convert our given angle into degrees as it is given in degrees and minutes.

We will divide 8 by 60 to convert 8 minutes into degrees as:

[tex]\frac{8}{60}=0.13333[/tex]

The doghouse, tower and angle of depression forms a right triangle with respect to ground, where, 331 feet is opposite side and x is adjacent side to angle 28.13 degrees.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(28.13^{\circ})=\frac{331}{x}[/tex]

[tex]x=\frac{331}{\text{tan}(28.13^{\circ})}[/tex]

[tex]x=\frac{331}{0.534623339864}[/tex]

[tex]x=619.12747783[/tex]

Upon rounding to nearest hundredth, we will get:

[tex]x\approx 619.13[/tex]

Therefore, the doghouse is 619.13 feet far from the foot of the tower.

Answer:

The girl will have $335,544.32

Step-by-step explanation:

2^25 = 33,554,432

Divide by 100 to turn the amount of pennies into dollars:

33,554,432/100

$335,544.32

Answer:

D. 348

Step-by-step explanation:

The volume of the square prisma is given by the following formula:

[tex]V = s^{2}h[/tex]

In which h is the height, and s is the side of the base.

Let's use implicit derivatives to solve this problem:

[tex]\frac{dV}{dt} = 2sh\frac{ds}{dt} + s^{2}\frac{dh}{dt}[/tex]

In this problem, we have that:

[tex]\frac{ds}{dt} = 5, \frac{dh}{dt} = -2, h = 7, s = 6[/tex]

So

[tex]\frac{dV}{dt} = 2sh\frac{ds}{dt} + s^{2}\frac{dh}{dt}[/tex]

[tex]\frac{dV}{dt} = 2*6*7*5 + (6)^{2}*(-2) = 348[/tex]

So the correct answer is:

D. 348

Answer:

P-value = 0.032794

Step-by-step explanation:

We are given the following information in the question:

Population mean, μ = 98.6 degrees

Sample size, n = 9

Alpha, α = 0.05

Test t-statistic = 2.132

The null and the alternate hypothesis :

[tex]H_{0}: \mu = 98.6\text{ degrees}\\H_A: \mu > 98.6\text{ degrees}[/tex]

We have to find the p-value for degree of freedom 8 and significance level 0.05

The calculated p-value is 0.032794

The null hypothesis in this considered experiment is: There is no change in their political beliefs as they go through college.

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

Here, it is specified that the scientist wants to study if students political beliefs change as they go through college. He wants to test if there are changes in the proportions of people who are liberal( or conservative).

Given that:

100 students before and after were asked their policial belief, as shown in table:

                               Liberal                Conservative

After college              80                       20

Before college           85                       15

Proportion of liberal = 1 - proportion of conservatives

So we will symbolize the hypotheses in terms of one of them, let it be proportions of liberals.

Sample size = 100

Favorable cases = Number of people from sample who consider themselves liberal. = X (say)

Sample proportion is: [tex]\hat{p}_1 = \dfrac{X}{N} = \dfrac{80}{100} = 0.8[/tex]

Sample proportion is: [tex]\hat{p}_2 = \dfrac{X}{N} = \dfrac{85}{100} = 0.85[/tex]

Let p1 and p2 be the population proportion of people believing themself liberal after and before college respectively.

Then, the null hypothesis will assume that the claim of difference in belief the scientist wants to test is false, and therfore,

[tex]H_0: p_1 = p_2[/tex] or [tex]H_0: p_1 - p_2 = 0[/tex] (no difference, proportions are same, indicating that belief of students doesn't change much, as d)

Thus, the null hypothesis in this considered experiment is: There is no change in their political beliefs as they go through college.

Learn more about null and alternative hypothesis here:

https://brainly.com/question/18831983

Answer:

H0 as the proportions are not as per the given estimation

Step-by-step explanation:

Given that two hundred randomly selected people were asked to state their primary source for news about current events: (1) Television, (2) Radio, (3) Internet, or (4) Other.

The hypothesised distribution is with 10%, 30%, 50%, and 10% for news sources 1 through 4, respectively

To check whether this is correct, we need not do test for each proportion

Instead we can do hypothesis testing for chi square goodness of fit with

H0 as the proportions are not as per the given estimation