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 = 36 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 = 39 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 σ₁ = 6.4% and σ₂ = 5.8%.

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

(i) What is the level of significance?

0.05

State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

(ii) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

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.)

[I need assistance in finding the value of the sample test statistic, as well as finding (or estimating) the P-value.]

Answer 1

2)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(40.96/36 + 33.64/39)
sp = 1.4143

Test statistic,
z = (x1bar - x2bar)/sp
z = (15.2 - 19.7)/1.4143
z = -3.18

3)

P-value Approach
P-value = 0.0007