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Data Analysis and Decision Making (with Online Content Printed Acces Card) (4th Edition)

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Problem

Suppose you are sampling from a large population, and you ask the respondents whether they believe men should be allowed to take paid paternity leave from their jobs when they have a new child. Each person you sample is equally likely to be male or female. The population proportion of females who believe males should be granted paid paternity leave is 56%, and the population proportion of males who favor it is 48%. If you sample 200 people and count the number who believe males should be granted paternity leave, is this number binomially distributed? Explain why or why not. Would your answer change if you knew your sample was going to consist of exactly 100 males and 100 females?

Step-by-step solution

Here it is given that the sample of people is taken. Each person from a sample is equally likely to be male or female and each individual is asked to respond that whether he/she believe males should be allowed to take paid paternity leave from their jobs or not.

Comment

The proportion of females who believe that males should be granted paid paternity leave is and the population proportion of males who favor it is . That is, the probability that males favor this issue is and the probability that females favor this issue is .

Comment

Nowwe have to obtain the total number of people out of a sample of people who believe males should be granted paid paternity leave.

Comment

Since it is given that each person from a sample is equally likely to be male or female. This implies that the number of males or females can be found from the sample with same probability of . Thus considering it to a binomial situation, find the number of males and number of females using the function CRITBINOM .

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3/18/2020 Solved: Suppose you are sampling from a large population, and y... | Chegg.com

https://www.chegg.com/homework-help/data-analysis-and-decision-making-4th-edition-chapter-5-problem-39p-solution-9780538476126?trackid=310c… 2/4

Comment

Now choose function CRITBINOM from the formula bar of the Excel worksheet and

substitute the values of the parameters defined as:

- Number of trials that are .

- Probability of success, that is

- Desired probability corresponding to the value of number of success, that is

Comment

This implies that we have to find the value of corresponding to the probability expression . (Here is the binomial variate)

Comment

After computing the number of males and females, add both to get the total number of people in a sample. It is to be noted that it won’t be equal to the sample size, that is . Thus to make the sample size (total number of males and females) equal to , Goal Seek has to be applied.

Comment

Since a sample of people is taken therefore set the value of the cell C8 which contains total number of people (total population) in a sample to by using Goal Seek from the tool menu of Excel worksheet by changing the cell C6 which contains the number of males and cell C7 which contains the number of females.

Comment

The following table will be obtained; the formulae used are also defined in the table for the ease of understanding.

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Comment

Hence the total number of people out of a sample of people who believe males should be granted paid paternity leave is .

Comment

The total number of people out of a sample of people who believe males should be granted paid paternity leave is binomially distributed since it defines the number of successes for the event which results in two mutually disjoint outcomes for each trial, that is, either the issue is favored or not favored by each person from a given sample.

This satisfies the physical condition for the binomial distribution. Hence the number is binomially distributed.

Comment

The answer would not change even if we knew our sample was going to consist of exactly males and females because it is given that each person from a sample is equally likely to be male or female.

Comment

This implies that the number of males or females can be found from the sample with same probability of which in turn gives the equal number of males and females, that is, out of a sample of , we get males and females. Thus no change would be experienced in the answer.

Comment

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