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 = 30 U.S. cities. The sample mean for these cities showed that x1 = 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 x2 = 19.7% of the young adults had attended college. From previous studies, it is known that ????1 = 7.6% and ????2 = 5.8%.
What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference ????1 − ????2. Round your answer to two decimal places.)
(iii) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(b) Find a 90% confidence interval for ????1 − ????2. (Round your answers to two decimal places.)