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 n₁ = 32 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 = 18.7% of the young adults had attended college. From previous studies, it is known that σ₁ = 7.4% and σ₂ = 4.8%.

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

(b) What is the level of significance?

(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)

(d) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(e) Find a 90% confidence interval for μ₁ − μ₂.(Round your answers to two decimal places.)

lower limit ?
upper limit ?

Answer 1