Answer:
We must pick at least 8 individual boots to be sure of picking at least one matching pair as explained from the pigeon hole principle.
Step-by-step explanation:
From pigeonhole principle, if k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing 2 or more objects.
Now, since we have 7 pairs of similar looking boots, thus, number of single boots we have will be;
Number of single boots = 7 x 2 = 14
Now, if we select 7 boots from the 14,then there's a possibility of selecting exactly 1 from each pair. Thus, we will not get a matching pair.
Whereas if we select 8 boots from the 14 single boots, then by the pigeon hole principle, at least 2 of the boots will need to be from the same pair. Hence we can pick at least 8 individual boots to be sure of picking at least one matching pair.
To ensure getting a matched pair from a pile of 7 pairs of boots, you would need to pick eight individual boots. This is based on the counting principle in mathematics where in the worst-case scenario, each boot you pick could be from a different pair.
Explanation:The question is about probability and counting principles in mathematics, specifically about how to identify a matched pair of boots from a pile of similar looking pairs. In the pile, there are seven pairs of boots, which means there are 14 individual boots from seven different pairs.
Now, if you randomly pick one boot, it could be from any pair. If you pick a second boot, it could also be from any pair, including the same pair as the first one. But to be sure that you get a matched pair, you will have to pick up eight boots. This is because, in the worst-case scenario, you might pick seven different boots each from a different pair. Once you pick the eighth boot, it is guaranteed to match one of the earlier seven because there are only seven pairs.
The minimum number of individual boots that you must pick to be sure of getting a matched pair is eight.
Learn more about Counting Principle here:https://brainly.com/question/29594564
#SPJ11
ILL GIVE YOU BRAINLIST !!! *have to get it right * Find the slope of the line represented in the table.
Answer:
A. 5
Step-by-step explanation:
5 ÷ 1 = 5
10 ÷ 2 = 5
15 ÷ 3 = 5
Answer:
the slope should be 1/5.
Step-by-step explanation:
slope = change in y / change in x
2-1 = 1 = change in Y
10-5 = 5 = change in X
the slope should be 1/5.
apologies in advance if my answer is wrong or I explain badly.
-----------------------------------------------------------------------------------------------
hope this helps! <3
-----------------------------------------------------------------------------------------------
Edit! someone else answered the question. their answer is probably correct, so please ignore my incorrect answer :'D
Question 5 (1 point)
A barrel contains 1256 liters of water.
Water is leaking out of the barrel at a rate of 3 liters per minute. At this rate, how many liters of water will
the barrel have after 27 minutes?
A. 81
B. 30
C. 1175
D. 1337
Answer:
C. 1175
Step-by-step explanation:
At 3 liters per minute, the amount leaked in 27 minutes is ...
(3 L/min)(27 min) = 81 L
Then the amount remaining is ...
1256 L - 81 L = 1175 L
There will be 1175 liters in the barrel after 27 minutes.
A customer in a shoe store bought a pair of shoes that were on sale for $15.00. He gave the salesman a $20.00 bill. Since he did not have change, the salesman went to an adjoining store and asked the lady in charge to give him change. She obligingly gave him a $10.00 bill and two $5.00 bills. The shoe man then returned and gave the customer his shoes and $5.00 change. The customer left.
Up to this point the story is very ordinary, but here is where "the plot thickens."
After the customer left, the lady who gave the salesman the change came into the store and told him that the $20.00 bill was a counterfeit. He looked at the bill, agreed that it was indeed worthless, and immediately repaid her with a good $20.00 bill.
That night, as he was closing the store, the shoe man began thinking about what he had lost in this series of transactions.
What did he lose?
Answer:
He lost $5.
Step-by-step explanation:
When the customer gives him the $20, the salesman does not gain any money because it is fake.
Then, he gets real money summing up to $20. So he gains that, but then gives $5 away. Now he has $15.
Then, the lady tells him the $20 bill is fake, so he must give the lady $20. So, 15 - 20 = -5. He lost $5.
Answer: He lost $35. $15 for the pair of shoes and $20 for having to repay the joined store for the counterfit money.
Step-by-step explanation:
An ice cream truck began its daily route with 95 gallons of ice cream. The truck driver sold 78% of the
ice cream. How many whole gallons of ice cream were sold?
Answer:
74.1 or 74
Step-by-step explanation:
Cable Strength: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb. Using the sample information as given, construct a confidence interval for the mean breaking strength of the new steel cable.
Answer:
95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].
Step-by-step explanation:
We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.
Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.
Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean breaking weight = 768.2 lb
s = sample standard deviation = 15.1 lb
n = sample of cables = 45
[tex]\mu[/tex] = population mean breaking strength
Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.02 < [tex]t_4_4[/tex] < 2.02) = 0.95 {As the critical value of t at 44 degree
of freedom are -2.02 & 2.02 with P = 2.5%}
P(-2.02 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.02) = 0.95
P( [tex]-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }[/tex] , [tex]768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }[/tex] ]
= [763.65 lb , 772.75 lb]
Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].
Is this irrational or rational?
Answer:
irrational
Step-by-step explanation:
because √3 is irrational
Answer:
irational
Step-by-step explanation:
The school estimates attendance at the varsity basketball games to be between 200 and 275, inclusive. What is the most the percent error could be? Round your answer to the nearest hundredth.
Answer:37.5 %
Step-by-step explanation:
Given
School attendance varies between 200 and 275
Most percentage error arises when attendance of 275 students is expected but only 200 students are present
Percentage error[tex]=\frac{275-200}{200}\times 100=37.5\ \%[/tex]
Which rigid transformation would map the
pre-image ΔABC to the image ΔA'B'C'?
a rotation by 90°
a reflection
a translation to the right
a translation up
Answer:
A Reflection on Edg
Step-by-step explanation:
Answer:B reflection
Step-by-step explanation:
edg 2022
The he average U.S. daily internet use at home is two hours and twenty minutes. A sample of 64 homes in Soddy-Daisy showed an average usage of two hours and 50 minutes with a standard deviation of 80 minutes. We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average.
1. State the null and alternative hypotheses to be tested.
2. Compute the test statistic.
3. The null hypothesis is to be tested at 95% confidence. What do you conclude?
Answer:
a) Null hypothesis:[tex]\mu = 140[/tex]
Alternative hypothesis:[tex]\mu \neq 140[/tex]
b) [tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]
c) The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
Now we can calculate the p value, since we are conducting a two tailed test:
[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]
Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=170[/tex] represent the sample mean in minutes
[tex]s=80[/tex] represent the standard deviation
[tex]n=64[/tex] sample size
[tex]\mu_o =140[/tex] represent the value to verify
[tex]\alpha[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Part a
We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:
Null hypothesis:[tex]\mu = 140[/tex]
Alternative hypothesis:[tex]\mu \neq 140[/tex]
Part b
Since we don't know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]
Part c
The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
Now we can calculate the p value, since we are conducting a two tailed test:
[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]
Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes
The null hypothesis that the average internet usage in Soddy-Daisy is not significantly different from the U.S. average is rejected based on a computed z-score of 3, which falls outside the critical z-score values for a 95% confidence level. Therefore, the average internet usage in Soddy-Daisy is significantly different from the U.S. average.
Explanation:This problem pertains to the domain of statistical hypothesis testing. Let's first set up the null and alternative hypotheses:
Null hypothesis (H0): The average internet usage in Soddy-Daisy is not significantly different from the U.S. average. This can be represented as H0: m = 140 minutes.Alternative Hypothesis (H1): The average internet usage in Soddy-Daisy is significantly different from the U.S. average. This can be represented as H1: m ≠ 140 minutes.For the second part, we need to compute the test statistic. The formula for the test statistic (z) in this context is z = (x - μ) / (σ/√n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.
So, (170-140) / (80/√64) = 30 / (10) = 3. The z score is 3.
For the final part of your question, with 95% confidence, the critical z-score values are -1.96 and +1.96. Since our observed z-score of 3 is outside this range, we reject the null hypothesis. Therefore, we can conclude that the average internet usage in Soddy-Daisy is significantly different from the U.S. average.
Learn more about Statistical hypothesis testing here:https://brainly.com/question/34698067
#SPJ3
what is the range of g(x)=3|x-1|-1?
The range of g(x) = 3|x-1|-1 is (-∞,∞).
What is range?The range is "set of all y-coordinates of the function's graph".
According to the question,
g(x) = 3 |x-1| - 1
To find range of linear polynomial 3|x-1|-1 put any value in right 'x' we can able to get any value 'y' in the set (-∞.∞).
Hence, the range of g(x) = 3|x-1|-1 is (-∞,∞).
Learn more about range here
https://brainly.com/question/15234445
#SPJ2
(i) If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of 0.1.
(ii) If volume is low this week then it will be high next week with a probability of 0.4. The manager estimates that the volume is five times as likely to be high as to be low this week.
Assume that state 1 is high volume and that state 2 is low volume.
(1) Find the transition matrix for this Markov process.(2) If the volume this week is high, what is the probability that the volume will be high two weeks from now?
A Markov chain is used to model this situation. The transition matrix based on the given probabilities will be [[0.9, 0.1],[0.4, 0.6]]. Also, to calculate the probability of being in a high-volume state two weeks from now given that it is in a high-volume state now, we square the matrix and look at the upper-left entry.
Explanation:A Markov process, in particular, a Markov chain, is a stochastic process that undergoes transitions from one state to another on a state space following the Markov property, stating that future states depend only on the current state and not on events that occurred before it. The transition matrix in these cases provides the probabilities between state transitions.
Given the data:
The probability of switching from hia gh volume (state 1) to a high volume (state 1) is 0.9The probability of switching from high volume (state 1) to low volume (state 2) is 1-0.9 =0.1The probability of switching from low volume (state 2) to high volume (state 1) is 0.4The probability of switching from low volume (state 2) to low volume (state 2), therefore, is 1-0.4 = 0.6Based on these probabilities the transition matrix will be of the form:
[[0.9, 0.1],[0.4, 0.6]].
To find the probability that the volume will be high two weeks from now, we will need to square the matrix as we are considering two steps ahead. The top left element of the resulting matrix will give the desired probability. In general, the i,j-th entry of the square of a transition matrix gives the 2-step transition probability from state i to state j.
Learn more about Markov Chain here:https://brainly.com/question/30465344
#SPJ11
find the slope passing through to two points -5, 2 and 7,-1
PLEASE HURRY
Answer:
-1/4
Step-by-step explanation:
The slope is found by
m = (y2-y1)/(x2-x1)
= (-1-2)/(7- -5)
= (-1-2)/(7+5)
= -3/12
= -1/4
Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.
Find the probability:
The probability that Joshua beats Eric in ping pong AND pool?
The probability that Joshua beats Eric in ping pong OR pool?
Answer:
P(pp & pool) = 22%
There is 22% probability that Joshua beats Eric in ping pong AND pool.
P(pp OR pool) = 50%
There is 50% probability that Joshua beats Eric in ping pong OR pool.
Step-by-step explanation:
The probability Joshua beats Eric in ping pong is given by
P(pp) = 0.48
The probability Joshua beats Eric in pool is given by
P(pool) = 0.46
The probability that Joshua beats Eric in ping pong AND pool is given by
P(pp & pool) = P(pp)×P(pool)
P(pp & pool) = 0.48×0.46
P(pp & pool) = 0.22
P(pp & pool) = 22%
Therefore, there is 22% probability that Joshua beats Eric in ping pong AND pool.
The probability that Joshua beats Eric in ping pong OR pool is given by
P(pp OR pool) = P(pp)×0.52 + P(pool)×0.54
Where 0.52 is the probability that Eric beats Joshua in the ping pong match (1 - 0.48 = 0.52)
Where 0.54 is the probability that Eric beats Joshua in the pool match (1 - 0.46 = 0.54)
P(pp OR pool) = 0.48×0.52 + 0.46×0.54
P(pp OR pool) = 0.25 + 0.25
P(pp OR pool) = 0.50
P(pp OR pool) = 50%
Therefore, there is 50% probability that Joshua beats Eric in ping pong OR pool.
To calculate the probability of Joshua beating Eric in at least one game of ping pong or pool, taking into account the probabilities for each game.
Probability plays a key role in analyzing the chances of events happening. In this case, we have two independent events: winning ping pong and winning pool. The probability of Joshua winning at least one game can be calculated using the probabilities given for each game.
Calculate the probability of Joshua winning both games: 0.48 × 0.46 = 0.2208
Subtract this value from 1 to find the probability of Joshua winning at least one game: 1 - 0.2208 = 0.7792
Therefore, Joshua has a 77.92% chance of beating Eric in at least one of the games.
An auto repair shop charges $50 plus $25 per hour. How much money would you have to pay if your car takes 4 hours to get repaired?
Answer:
150
Step-by-step explanation:
Answer: You would pay $150
Step-by-step explanation: Take 25 times 4, then add on the additional fee.
A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sample of 46 bins, the sample mean amount was 49.9 pounds and the sample standard deviation was 3.641 pounds. Construct a 95.7% confidence interval for the expected amount of garbage per bin for all bins in the city. Answer to 3 decimals (a) What is the lower limit of the 95.7% interval
Answer:
The 95.7% confidence interval for the expected amount of garbage per bin for all bins in the city
(48.937 , 50.863)
Step-by-step explanation:
Explanation:-
Given data random sample of 46 bins, the sample mean amount was 49.9 pounds and the sample standard deviation was 3.641
The sample size 'n' =46
mean of the sample x⁻ = 49.9
Standard deviation of the sample S = 3.641
Confidence intervals:-
The 95.7% confidence interval for the expected amount of garbage per bin for all bins in the city
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
Degrees of freedom = n-1 = 46-1 =45
The tabulated value t₀.₉₆ = 1.794 ( from t-table)
[tex](49.9 - 1.794 \frac{3.641}{\sqrt{46} } ,49.9+ 1.794 \frac{3.641}{\sqrt{46} })[/tex]
(49.9 -0.9630 , 49.9+0.9630)
(48.937 , 50.863)
Conclusion:-
The 95.7% confidence interval for the expected amount of garbage per bin for all bins in the city
(48.937 , 50.863)
An association was formed by students to protest labor exploitation in the apparel industry. There were 18 student "sit-ins" for a "sweat-free campus" organized at several universities. Data were collected for the duration (in days) of each sit-in, as well as the number of student arrests. The data for 5 sit-ins in which there was at least one arrest and the results of a simple linear regression are found below. Let y be the number of arrests and x be the duration. Complete parts a through d Click the icon to view the data table E Click the icon to view the results of the simple linear regression. a. Write the equation of a straight-line model relating y to x.A. y = beta1xB. y = beta1x^2 + beta0C. y = beta0 + beta1x + {D. y = beta1x + {b. Use the results of the linear regression to find the least squares prediction equation Type an integer or decimal rounded to three decimal places as needed)
Data for complete question is attached.
Answers
Therefore .
A. The regression equation is
y = beta0 + beta1+ ∈
B. From the given output regression line
y= 2.478+7.717x
The question addresses using a simple linear regression model to determine the relationship between two variables, and how to interpret the parameters of that model, as well as the significance of the correlation coefficient in the context of a hypothetical student protest situation.
Explanation:The subject of this question is about linear regression analysis in mathematics, particularly in the context of statistical analysis. The question demonstrates the application of a simple linear regression to decipher the relationship between the duration of student sit-ins (independent variable) and the number of arrests (dependent variable).
Answers to the Linear Regression Exercise:The equation of the straight-line model relating number of arrests (y) to duration (x) is C. y = beta0 + beta1x, where beta0 is the y-intercept, and beta1 is the slope of the regression line.To find the least squares prediction equation, use the provided regression output to plug in the estimated coefficients for the y-intercept (beta0) and slope (beta1). The form it should take is ý = a + bx, where 'a' is the estimated y-intercept and 'b' is the estimated slope.The y-intercept, or the constant 'a', has meaning if it has a context within the scope of the study. For example, it might represent the expected number of arrests when the duration of the sit-in is zero, if such a scenario makes sense within the context of the study.To find the correlation coefficient, typically denoted as 'r', refer to the regression output and assess its significance level. A significant correlation coefficient indicates a strong relationship between the dependent and independent variables.What is the area of a circle with a radius of 7 cm? (Use 3.14 for x and round to the nearest tenth.)
38.5 cm
44.0 cm
150 cm?
153.9 cm?
Answer:
153.9 cm
Step-by-step explanation:
A = pi(r²)
= 3.14(7²)
= 3.14(49)
= 153.86
= 153.9 cm
In a certain normal distribution of scores, the mean is 40 and the standard deviation is 3. Find the s-score corresponding to a score
of 54.
a. 4.67
C. 4.67
b. 18.0
d. 13.33
Please select the best answer from the choices provided
Answer:
The s-score corresponding to a score of 54 is 4.67
Step-by-step explanation:
In a certain normal distribution of scores:
Mean = [tex]\mu = 40[/tex]
Standard deviation = [tex]\sigma = 3[/tex]
We are supposed to find the z-score corresponding to a score of 54.
Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]
x=54
Substitute the values
So,[tex]Z= \frac{54-40}{3}[/tex]
Z=4.67
So, Option A is true
Hence the s-score corresponding to a score of 54 is 4.67
Find the dot product of the given vectors.
u=2i−6j
v=3i+9j
u = 2i - 6j
v = 3i + 9j
Take the dot product:
u • v = (2i - 6j) • (3i + 9j)
u • v = (2i • 3i) + (2i • 9j) + (-6j • 3i) + (-6j • 9j)
u • v = 6 (i • i) + 18 (i • j) - 18 (j • i) - 54 (j • j)
The dot product is defined so that for the orthogonal unit vectors i and j, we have i • i = j • j = 1, and i • j = 0. So the above reduces to
u • v = 6 + 0 - 0 - 54
u • v = -48
In a 2008 article by Hsiu-Ling Lee, data from 147 colleges from 1995 to 2005 were used to predict endowments to a college from the average SAT score of students attending the college, among other variables. The resulting regression equation for these variables was Ŷ = –20.46 + 4.06(X). Using the regression equation, what would be the endowments (in billions) to a college whose students' average SAT score is 1050?
Answer:
4283.46 billion
Step-by-step explanation:
According to the information of the problem
[tex]\hat{Y} = 20.46 + 4.06(X)[/tex]
Therefore you are looking for
[tex]\hat{Y} = 20.46 + 4.06(1050) = 4283.46[/tex]
how do i Find the volume of the composite figure.
4 ft2 ft7 ft5 ft2 ft
The volume of the composite figure is cubic feet.
Answer:
You have to break apart the shape into individual shapes to find the volume of each one. Then you add.
hope this helped :)
A hot air balloon rising vertically is tracked by an observer located 4 km from the lift‑off point. At a certain moment, the angle between the observer's line of sight and the horizontal is π/5, and it is changing at a rate of 0.4 rad/min. How fast is the balloon rising at this moment? Let y be the height of the balloon (in km), t be time (in minutes), and θ the angle between the line‑of‑sight and the horizontal (in radians).
Answer:
1.22 km/min
Step-by-step explanation:
Let Q be baloon height at a time t. Our goal is to determine the speed of the baloon at the moment.
The dy / dt velocity of the baloon when = π/5?
So we can restate the question as follows:
Owing to the fact d / dt = 0.2 rad / min at some stage = π/5
from fig:
tanθ = y/4
Differentiating w.r.t "t"
sec2 θ * dθ/dt = 1/4(dy/dt)
=> dy/dt = (4/cos2 θ)dθ/dt
At the given moment θ = and dθ/dt = 0.2 rad/min.
dy/dt = (4/cos2)* (0.2)
= 1.22 km/min
And the velocity of the baloon currently is 1.22 km / min.
Need help solving this equation -3(c-1)=33
Answer:
c= -10
Step-by-step explanation:
-3(c-1)= 33
-3(c) -3(-1)= 33 (expand)
-3c +3= 33
-3c= 33-3 (-3 on both sides)
-3c= 30 (simplify)
3c= -30 (divide by -1 throughout)
c= -30 ÷3
c= -10
mDE = 115 and mbc =42. Find m
It has long been stated that the mean temperature of humans is 98.6 degrees F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F. They measured the temperatures of 56 healthy adults 1 to 4 times daily for 3 days, obtaining 250 measurements. The sample data resulted in a sample mean of 98.2 degrees F and a sample standard deviation of 0.9 degrees F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6 degrees F at the alpha = 0.01 level of significance.1. State the hypotheses.A. Upper H 0H0:▼▼ 98.6 FB. Upper H 1H1:▼▼ 98.6 F2. Find the test statistic.a. t0 = ?b. the P-value is:____.3. What can be concluded?A. RejectUpper H0 since the P-value is less than the significance level.B. Reject Upper H0 since the P-value is not less than the significance level.C. Do not reject Upper H0 since the P-value is less than the significance level.D. Do not reject Upper H0 since the P-value is not less than the significance level.
Answer:
Reject null hypothesis ([tex]H_0[/tex]) since the P-value is less than the significance level.
Step-by-step explanation:
We are given that it has long been stated that the mean temperature of humans is 98.6 degrees F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F.
The sample data resulted in a sample mean of 98.2 degrees F and a sample standard deviation of 0.9 degrees F.
Let [tex]\mu[/tex] = mean temperature of humans.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu\geq[/tex] 98.6°F {means that the mean temperature of humans is more than or equal to 98.6°F}
Alternate Hypothesis, [tex]H_A[/tex] : p < 98.6°F {means that the mean temperature of humans is less than 98.6°F}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean temperature = 98.2°F
[tex]\sigma[/tex] = sample standard deviation = 0.9°F
n = sample of healthy adults = 56
So, test statistics = [tex]\frac{98.2-98.6}{\frac{0.9}{\sqrt{56} } }[/tex] ~ [tex]t_5_5[/tex]
= -3.326
The value of t test statistics is -3.326.
Now, P-value of the test statistics is given by following formula;
P-value = P( [tex]t_5_5[/tex] < -3.326) = 0.00077 or 0.08%
Since, P-value of the test statistics is less than the level of significance as 0.08% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean temperature of humans is less than 98.6°F.
To determine if the mean human temperature is less than 98.6°F, we conducted a left-tailed t-test using the provided sample data. We calculated the t-test statistic and then used it to find the p-value. We then used the p-value to make our final decision on whether to reject or fail to reject our null hypothesis.
Explanation:In this scenario, we are performing a hypothesis test about the average human temperature. Let's formulate our hypothesis first:
Null hypothesis (H0): The average human temperature equals 98.6 F. Mathematically, H0: μ = 98.6 F.Alternative hypothesis (H1): The average human temperature is less than 98.6 F. Mathematically, H1: μ < 98.6 F.
We will conduct a left-tailed t-test because we are testing whether the average human temperature is less than a stated value.
Given the data: the sample size n = 250, the sample mean (x_bar) = 98.2 F, and the standard deviation (s) = 0.9 F.
To calculate the t-test statistic, use the formula: t0 = (x_bar - μ) / (s/√n)
For getting the p-value, you would use a statistical table or software with the above t statistic and degree of freedom (which is n-1 in this case).
In the end, if your p-value is less than the significance level (α = 0.01 in this case), we reject the null hypothesis, if not, we fail to reject the null hypothesis.
If the P-value is less than α, we would conclude that the research may be correct, and the average human temperature is indeed lower than 98.6 F (37.0 °C).
Learn more about Hypothesis Testing here:https://brainly.com/question/34171008
#SPJ11
Determine which numbers could not be used to represent the probability of an event. Select all that apply. A. StartFraction 64 Over 25 EndFraction , because probability values cannot be greater than 1. B. 0.0002, because probability values must be rounded to two decimal places. C. minus1.5, because probability values cannot be less than 0. D. 0, because probability values must be greater than 0. E. 33.3%, this is because probability values cannot be greater than 1. F. StartFraction 320 Over 1058 EndFraction , because probability values cannot be in fraction form.
Answer:
A. [tex]\frac{64}{25}[/tex] , because probability values cannot be greater than 1.
C. -1.5, because probability values cannot be less than 0.
Step-by-step explanation:
Probability is the extent to which an event is likely to happen. It ranges from 0(impossible) to 1(certain). Probability values can be written in decimal form or in fractional form.
The following numbers could not be used to represent the probability of an event.
A. [tex]\frac{64}{25}[/tex] , because probability values cannot be greater than 1.
C. -1.5, because probability values cannot be less than 0.
Who to write 26.46 as a fraction?
Answer:
2646/100 or 260 46/100 or 260 23/50
if you sell a stock for more money than you paid for it, you have a gross capital loss. true or false
Answer:False
Step-by-step explanation:
False
Whenever a stock is sold more money than what is paid for it is termed as Gain or profit
For example if an item is bought for [tex]\$100[/tex] and it is sell for [tex]\$120[/tex]
then there is a profit of
[tex]\Rightarrow \frac{120-100}{100}\times 100[/tex]
[tex]\Rightarrow 20\%[/tex]
or a gain of [tex]\$20[/tex]
Answer: The answer is False, i know this because i took this quiz on edge and it was correct as false <3 hope this helps
Step-by-step explanation: brainliest please :3
there is an antenna on the top of a building. From a location 300 ft from the base of the building, the angle of elevation to the top of the building is measured to be 40 degrees. From the same location the angle of elevation to the top of the antenna is measured to be 43 degrees. find the height of the antenna
Answer:
300tan43 - 300tan40
Step-by-step explanation:
Use tangent to find the height of the building:
tan40 = b/300
b = 300tan40
The use tangent to find the height to the top of the antenna:
tan43 = a/300
a = 300tan43
The antenna height = a - b
A file consisting of X packets is sent over the network to an end user. It is known that X is a random variable with PMF PX(x) = cx2 for x = 1, 2, 3, 4; and PX(x) = 0 otherwise. Each packet is received correctly with probability p, independently of the other packets. a) Find the constant c. b) Find P[X > 2]. c) Find the probability that the entire file is received correctly, i.e., all X packets are received correctly
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for the step by step solution of the given problem.