Question

A random sample of 88 women showed that the mean number of children reported was 1.58 with a standard deviation of 1.8. (interestingly, a sample of 88 men showed a mean of 1.3 children.) Complete parts (a) through (c) below EEB Click the lcon to view the ttable. Find a 95% confidence interval for the population mean number of children for women. Because the sample size is so large, you can use 1.96 for the critical value of t (which is the same as the critical value of z) if you do the calculations manually. Choose the correct answer below and, if necessary, fill in the answer boxes to (Type integers or decimals rounded to the nearest hundredth as needed. Use ascending order.) OA.ee are 95% confident that the sample mean number of children is betweenland n complete your choice. k ch Co O B We are 95% confident that the population mean number of children is between and m, OC. There is a 95% chance that all numbers of children will be between-and O D. The requirements for constructing a confidence interval are not satisfied. b Find a 90% confidence interval. Use 1.645 for the critical value of t, which is the critical value ofz.choose the correct answer below and, if necessary, fill in the dia 1 answer boxes to complete your choice (Type integers or decimals rounded to the nearest hundredth as needed. Use ascending order.) OA. OB. we are 90% confident that the population mean number of children is between land There is a 90% chance that all numbers of children will he hetween ed . and Tool Click to select your answer Sample tests and quizzes can be taken for practice or to build your study plan. Sample tests and quizzes do not affect your grade. doTest(186441665,%20falseh" You have no sample assignments.

Answer 1

Solution:

a. Find the 95% confidence interval for the population mean number of children for women.

Answer: The correct option is B.

B. We are 95% confident that the population mean number of children is between 1.20 and 1.96

b. Find the 90% confidence interval

Answer: The correct option is A

A. We are 90% confident that the population mean number of children is between 1.26 and 1.90

c. Which interval is wider and why?

Answer: The correct option is C

C. The 95% confidence interval is wider because it has a greater confidence level, and therefore we use a greater standard error, which creates a wider interval.