Stats 250 W12 Exam 2 Solutions 1. Age at first marriage – A researcher investigating changing trends in marriage wants to determine if the average age of first marriage is higher for men than for women. He takes a random sample of 30 recently married heterosexual couples from a list of newspaper wedding announcements and records the ages of the man and woman for each couple. An excerpt of the data is shown below: Couple Male age Female age Difference (M – F) 1 27.3 27.6 -0.3 2 28.5 27.8 0.7 … 30 30.7 32.4 -1.7 Mean 28.2 27.6 0.65 Standard Deviation 2.8 3.2 1.5 a. State the appropriate hypotheses to test the researcher's theory and complete the definition of the corresponding parameter. The research has decided to use a 5% significance level. [3] H0: ____ µd= 0 _________________ Ha: ________ µd> 0 _____________________ where the parameter represents the population mean difference ___in age at first marriage (m – f) for all couples ________ Results from R for a two sided test(this may or may not match your answer in part a) are provided below: Summary Statistics Mean diff (𝒅𝒅�) Std. Dev (sd) Sample size (n) Std. Error .65 1.50 30 .2746 Paired T Results t df p-value 95% CI Lower 95% CI Upper 2.37 29 0.024 .09 1.21 b. Use the R output to complete the statement by filling in the blank and circling the appropriate word: [2] The observed sample mean difference in ages is ____ 2.37 ________ standard errors (Circle one) ABOVE BELOWthe hypothesized population mean difference in ages. c. If there really is no difference in the average age of first marriage for men and women in the population of all such couples, what is the expected value of the test statistic? [1] Final answer _______ 0 _______ d. Provide a complete sketch of the p-value; include a label and values on the x axis, a full label for the distribution, the shaded area for the p-value, and the actual value of the p-value [4] p-value = ____0.024/2 = 0.012____________ e. Circle the appropriate statistical decision: Reject H0Fail to reject H0[1] f. What type of error could the researcher have made? [1] (circle one) Type I Error Type II Error Cannot be determined Page 1

Stats 250 W12 Exam 2 Solutions 2. Caffeine Consumption – Concerned about caffeine consumption by young adults, a doctor decides to investigate the caffeine consumption of college students and high school students. She randomly samples 72 college students (group 1) and 64 high school students (group 2) to investigate if the mean caffeine consumption (in mg) differs between college students and high school students. It has been a few years since she took her statistics course, so she uses Google to find a few commands in R and obtains the output below: Summary Statistics Group Mean Std. Dev Sample Size General Std. Error Pooled Std. Error College 168.73 60.97 72 9.43 9.56 Female 149.84 48.89 64 Levene’s Test: F = .714, p-value = .400 a. The researcher wishes to estimate the difference in population mean caffeine consumption (college – high school) using a 95% confidence interval. She would like to use the pooled procedure. She notes that the two sample standard deviations are somewhat similar, but would like to be further assured by examining Levene’s Test results.