Chapter 10.2, Problem 14P

Please provide the following information for Problems 11-22. part (a):

(i) What is the level of significance? State the null and alternate hypotheses.

(ii)Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.

(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 a?

(v)Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount, and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.

Generation Gap: Education 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 $n_1=32$ U.S. cities. The sample mean for these cities showed that $x_1=15.2\%$ of the older adults had attended college. Large surveys of young adults (age 25-34) were taken in $n_2=35$ U.S. cities. The sample mean for these cities showed that $x_2=19.7\%$ of the young adults had attended college. From previous studies, it is known that ${\sigma }_1 =7.2\%\text{ and }{\sigma }_{\text{2}} =5.2\%$ (Reference: American Generations, S. Mitchell).

(a) Does this information indicate that the population mean percentage of young adults who attended college is higher? Use a = 0.05.

(b) Find a 90% confidence interval for ${\mu }_1-{\mu }_2.$ Explain the meaning of the confidence interval in the context of the problem.