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 = 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 = 18.7% of the young adults had attended college. From previous studies, it is known that σ₁ = 7.2% and σ₂ = 4.8%.

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.)


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

b) Find a 90% confidence interval for

μ₁ − μ₂.

(Round your answers to two decimal places.)

lower limit
upper limit

Answer 1

The statistical software output for this problem is:

Hence,

a) ii) Test statistic = -2.27

iii) P - value = 0.0117

b) 90% confidence interval:

Lower limit = -6.04

Upper limit = -0.96