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5. In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 43 years. a. Write out the appropriate hypotheses. b. We plan to test our hypothesis by selecting a random sample of 64 men who married for the first time last year. Do you think the necessary assumptions for inference (such as for testing of hypothesis and for constructing confidence interval) are satisfied? Explain. C. Write down the approximate sampling distribution of the sample statistic in your answer sheet by replacing the symbols below by numbers that you know from the information given. X~ Normal (μ, o/√n)

5. In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 43 years. a. Write out the appropriate hypotheses. b. We plan to test our hypothesis by selecting a random sample of 64 men who married for the first time last year. Do you think the necessary assumptions for inference (such as for testing of hypothesis and for constructing confidence interval) are satisfied? Explain. C. Write down the approximate sampling distribution of the sample statistic in your answer sheet by replacing the symbols below by numbers that you know from the information given. X~ Normal (μ, o/√n)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5. In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 43 years. a. Write out the appropriate hypotheses. b. We plan to test our hypothesis by selecting a random sample of 64 men who married for the first time last year. Do you think the necessary assumptions for inference (such as for testing of hypothesis and for constructing confidence interval) are satisfied? Explain. Write down the approximate sampling distribution of the sample statistic X in your answer sheet by replacing the symbols below by numbers that you know from the information given. X~ Normal (μ, o/ √n) d. The men in our sample married at an average age of 24.2 years with a standard deviation of 5.3 years. Carry out an appropriate test at 1% significance level, using the critical value approach. That is, find the appropriate critical region, make decision and write your conclusion. Find the p-value for the test and make sure that your acceptance-rejection decision remains the same if the p-value approach is adopted. Explain in your own words and as explained in class, how you interpret this p-value. Without doing any calculations, explain what would happen if i) C. e. f. g. h. i. Ha: μ = 27.0. Would the power increase or decrease against this new alternative? Explain. ii) Old alternative remains, but sample size is increased. Would the power increase or decrease? Explain. Find a 99% confidence interval for the for the unknown population average age at marriage. Explain in your own words and as explained in class what you mean by this confidence interval. Now write a two-tailed test with the appropriate null and alternative hypotheses for problem in (a) through (d). Is 23.3 included in the 99% confidence interval you created in (a) above? Whatever may be the case, explain the implications clearly.
Transcribed Image Text:5. In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 43 years. a. Write out the appropriate hypotheses. b. We plan to test our hypothesis by selecting a random sample of 64 men who married for the first time last year. Do you think the necessary assumptions for inference (such as for testing of hypothesis and for constructing confidence interval) are satisfied? Explain. Write down the approximate sampling distribution of the sample statistic X in your answer sheet by replacing the symbols below by numbers that you know from the information given. X~ Normal (μ, o/ √n) d. The men in our sample married at an average age of 24.2 years with a standard deviation of 5.3 years. Carry out an appropriate test at 1% significance level, using the critical value approach. That is, find the appropriate critical region, make decision and write your conclusion. Find the p-value for the test and make sure that your acceptance-rejection decision remains the same if the p-value approach is adopted. Explain in your own words and as explained in class, how you interpret this p-value. Without doing any calculations, explain what would happen if i) C. e. f. g. h. i. Ha: μ = 27.0. Would the power increase or decrease against this new alternative? Explain. ii) Old alternative remains, but sample size is increased. Would the power increase or decrease? Explain. Find a 99% confidence interval for the for the unknown population average age at marriage. Explain in your own words and as explained in class what you mean by this confidence interval. Now write a two-tailed test with the appropriate null and alternative hypotheses for problem in (a) through (d). Is 23.3 included in the 99% confidence interval you created in (a) above? Whatever may be the case, explain the implications clearly.
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