Education influences attitude and lifestyle. Differences in education are a big factor in the “generation gap.” Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n1 = 32 U.S. cities. The sample mean for these cities showed that 1 = 15.2% of the older adults had attended college. Large surveys of young adults (age 25–34) were taken in n2 = 35 U.S. cities. The sample mean for these cities showed that 2 = 19.7% of the young adults had attended college. From previous studies, it is known that σ1 = 7.2% and σ2 = 5.2%.
(a) Does this information indicate that the population mean percentage of young adults who attended college is higher? Use α = 0.05.
(b) Find a 90% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) – (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.