Question

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 - 34 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 ny = 32 U.S. cities. The sample mean for these cities showed that X2 = 18.2% of the young adults had attended college. From previous studies, it is known that, 6.4% and on = 4.2%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho! Mi < 2; H: 1 2 Hoi H - H2 H H1 H2 O Ho: Ag - H2i Hy: My < $2. Оно и на них на (b) What sampling distribution will you use? What assumptions are you making The Student's t. We assume that both population distributions are approximately normal with known standard deviations The standard normal. We assume that both population distributions are approximately normal with known standard deviations The student'st. We assume that both population distributions are approximately normal with untown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations What is the value of the sample test statistic (st the difference. Round your answer to two decimal places) (c) Find (or estimate the value Round your answer to four decimal aces)

Answer 1

a)

Based on the information provided, the significance level is a = 0.05

The following null and alternative hypotheses need to be tested: Ho: Mi = 12 Ha: uli<H12

b)

Option B.

test statistic value is

2= X1 - X, Voni+o/n2 15.2 – 18.3 6.42/34 + 4.22/32 -2.339

p value = p(z<-2.339) = 0.0097

Using the P-value approach: The p-value is p=0.0097, and since p=0.0097 < 0.05, it is concluded that the null hypothesis is rejected.