A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 500 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.47.

(a) What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 ?

The polling agency will take another sample from a different region, Region B, of the city. The agency plans to select a random sample of 400 voters. Assume that the population proportion of voters who would support the ballot measure in Region B is 0.51.

(b) Describe the sampling distribution of the difference in sample proportions (Region B minus Region A).
(c) What is the probability that the two sample proportions will differ by more than 0.05 ?

Answers

Answer 1
Final answer:

To estimate the probability of a sample proportion being greater than 0.50 in Region A and the sampling distribution of the difference in sample proportions between two regions, we use normal approximation and the Central Limit Theorem, involving statistical calculations based on known population proportions and sample sizes.

Explanation:

To answer whether a polling agency's investigation into voter support for a ballot measure will have a sample proportion greater than 0.50 in Region A and to describe the sampling distribution of the difference in sample proportions (Region B minus Region A), including the probability that the two sample proportions differ by more than 0.05, we follow a statistical approach based on the Central Limit Theorem.

For Region A, assuming a population proportion of 0.47 and a sample size of 500, the probability of the sample proportion supporting the ballot measure being greater than 0.50 can be calculated using the normal approximation. This involves finding the z-score for the sample proportion and then using the standard normal distribution to find the associated probability.

For the sampling distribution of the difference in sample proportions (Region B minus Region A), we need to combine the variances of both sample proportions due to the Central Limit Theorem. This allows us to assess the probability that the two sample proportions will differ by more than 0.05 using a similar z-score and standard normal distribution approach.

The techniques applied involve the use of normal approximation to calculate probabilities and assumes a large enough sample size for the approximation to be accurate.


Related Questions

a 150 lb man has 2 beers, determine his BAC
BAC = ?​

Answers

Answer: BAC = 0.056%

Explanation:-

Data given;

Weight of the man = 150 lbs (Wt)

Number of drinks = 2 beers

We know that

A beer contains 5% (0.05) of alcohol (D)

1 bear = 12oz

So 2 beer = 2 × 12 = 24oz (A)

Derived from widmark formula;

BAC for Male = (A × D × 5.14) / ( Wt × 0.73 )

BAC for Female = (A × D × 5.14) / ( Wt × 0.66 )

WHERE

A = Alcohol consumed in ounces (oz.)

D = percentage of alcohol written as a decimal

Wt = weight of person in pounds (lbs.)

Using BAC for male

BAC for Male = (A × D × 5.14) / ( Wt × 0.73 )

We simply input our values

BAC = ( 24 × 0.05 × 5.14) / ( 150 × 0.73)

BAC = 6.168 / 109.5

BAC = 0.056%

An ocean basin will form in what location, relative to the major tectonic plates?

Answers

Final answer:

Ocean basins can form at rift basins where continental crust is pulled apart and subsequently subsides, or at subduction zones where one plate dives beneath another. Ocean basins influence the size and movement of tectonic plates and can close over time, possibly leading to supercontinent formation.

Explanation:

An ocean basin is likely to form at a location where continental crust is being pulled apart due to the process of rift basin formation. As the crust on both sides of the rift subsides, the area initially becomes a narrow sea and, if rifting continues, eventually develops into an ocean basin. The East African rift basin is an example of an early stage in this process. Additionally, other types of basins such as trench basins, forearc basins, and foreland basins are associated with different tectonic settings such as subduction zones and the mass of volcanic ranges.

Ocean basins are relatively young geological features, not exceeding 180 million years in age. The formation of ocean basins can significantly influence the size of oceanic and continental plates, such as the expansion of the Atlantic Ocean due to the mid-Atlantic ridge spreading, which is not counteracted by subduction except in certain regions like the Caribbean. In contrast, the Pacific Ocean is slowly getting smaller because its formation rate is outpaced by subduction processes, such as under North America at the Cascadia Subduction Zone.

Over geological time, as oceanic crust subducts beneath continental crust, ocean basins can close, leading to continental collision and the potential formation of a supercontinent. Known cycles of supercontinent formation and breakup have occurred throughout Earth's history approximately every 500 million years.

Other Questions
What theory explains the formation and movement of the outer surface of the Earth? A. the theory of natural selection B. the theory of plate tectonics C. the theory of atmospheric layers D. the theory of glacier movement 1.Find the Length of Line AD A(6, 2) D(-3, -2) The balance in retained earnings at December 31, 2017 was $1,440,000 and at December 31, 2018 was $1,164,000. Net income for 2018 was $1,000,000. A stock dividend was declared and distributed which increased common stock $500,000 and paid-in capital $220,000. A cash dividend was declared and paid. Reference: Ref 23-4 The amount of the cash dividend was A. $496,000. B. $1,276,000. C. $556,000. D. $776,000. OLHeuveWhich of these statements is NOT true?A. Advertising is not a contributing factor for underaged alcohol drinkingB. Teens are more likely to have unprotected sex when drinking alcohol,C. About 28% of high school seniors are binge drinkers.D. Underaged drinkers are more likely to contract a sexually transmitted diseasePlease select the best answer from the choices provided. Please, answer, I need help. Which statement best explains the situational irony thatoccurs in the passage?The aunt wants the bachelor to tell a good story, but hedoes notThe bachelor fears that the children will not like hisstory, but they do.The bigger girl does not expect the bachelor to tell astory, but he does.The aunt does not expect the bachelor to tell a story,but he does. What is the area of the right triangle The rule of thirds states that:A) digital designs should have three colors.B) digital designs should have three fonts.C) the eye naturally goes to the intersection of the lines that divide an image into thirdsD) the eye naturally goes to the three lightest places in an image, from top to bottom Solutions of sodium acetate and acetic acid are combined in equal volume to produce a buffer. Identify the combination that will produce the buffer with the highest buffer capacity. Select one: a. 0.01 M CH3COOH , 0.1 M CH3COONa b. 0.1 M CH3COOH , 0.1 M CH3COONa c. 0.1 M CH3COOH , 0.01 M CH3COONa d. 0.01 M CH3COOH , 0.01 M CH3COONa Whats the answer????????? Which is the solution to the inequality? One-fourth + x less-than StartFraction 5 over 6 EndFraction x less-than StartFraction 7 over 12 EndFraction x greater-than StartFraction 7 over 12 EndFraction x less-than 1 and StartFraction 1 over 12 EndFraction x greater-than 1 and StartFraction 1 over 12 EndFraction Find the midpoint of A and B where A has coordinates (2,4) and B has coordinates (-3,-9) What is the value of p in the equation of 2(3p -4) = 10 Which of the following statements is true of how emotion functions in conflict? Select one: a. Conflict is avoided if emotional arousal is high. b. Emotional events always trigger unfamiliar patterns of responses during conflict. c. Emotional behavior during conflict is unaffected by individual behavior. d. Maturity mediates strong emotion during conflict. e. The intensity of emotion remains constant through the conflict process. The emancipation proclamation affected the unions civil war efforts by If you help me get this right i will mark u as most brilliance! A ball is dropped from rest from a Cliff and falls for 3 seconds.Neglecting air resistance, the final velocity of the ball ism/s. (g = -9.8 m/s2)Enter the answer g (d) Usually, in the case of two finite-duration signals like in parts (a) and (b), the convolution integralmust be evaluated in 5 different regions: no overlap (on the left side), partial overlap (on the left side),complete overlap, partial overlap (on the right side), and no overlap (on the right side). In this case,there are only 4 regions. Why What had dill said he had been able to capture in his letter to scout Richard recently accepted a job as a truck driver for a large transportation company, but he wants to one day run the companys distribution center. What is Richards current educational level, and how can he best achieve his goal?Richard is a high school graduate with a special drivers license who could quit his job and earn a masters degree that meets his goals.Richard is a high school graduate with a special drivers license who could earn a bachelors degree and apprentice with his company.Richard is a high school graduate who could earn an associates degree and spend his off-hours completing an internship with his company.Richard is a high school graduate who could earn a vocational degree, complete an apprenticeship, and wait to advance with his company. Steam Workshop Downloader