Education influences attitude and lifestyle. Differences ineducation are a big factor in the \"generation gap.\" Is the youngergeneration really better educated? Large surveys of people age 65and older were taken in n₁ = 38 U.S. cities.The sample mean for these cities showed that x₁= 15.2% of the older adults had attended college. Large surveys ofyoung adults (age 25 - 34) were taken in n₂ =34 U.S. cities. The sample mean for these cities showed thatx₂ = 18.1% of the young adults had attendedcollege. From previous studies, it is known thatσ₁ = 7.2% and σ₂ = 5.4%.Does this information indicate that the population mean percentageof young adults who attended college is higher? Use α =0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ =μ₂; H₁:μ₁ >μ₂H₀:μ₁ < μ₂;H₁: μ₁ =μ₂     H₀:μ₁ = μ₂;H₁: μ₁ ≠μ₂H₀:μ₁ = μ₂;H₁: μ₁ <μ₂

(b) What sampling distribution will you use? What assumptions areyou making?

The Student's t. We assume that both populationdistributions are approximately normal with unknown standarddeviations.The standard normal. We assume that both populationdistributions are approximately normal with known standarddeviations.     The standard normal. Weassume that both population distributions are approximately normalwith unknown standard deviations.The Student's t. Weassume that both population distributions are approximately normalwith known standard deviations.

What is the value of the sample test statistic? (Test thedifference μ₁ − μ₂. Roundyour answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer tofour decimal places.)


Sketch the sampling distribution and show the area corresponding tothe P-value.

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.At theα = 0.05 level, we fail to reject the null hypothesis andconclude the data are statisticallysignificant.     At the α = 0.05level, we reject the null hypothesis and conclude the data are notstatistically significant.At the α = 0.05 level, we failto reject the null hypothesis and conclude the data are notstatistically significant.

(e) Interpret your conclusion in the context of theapplication.

Fail to reject the null hypothesis, there is insufficientevidence that the mean percentage of young adults who attendcollege is higher.Reject the null hypothesis, there is sufficientevidence that the mean percentage of young adults who attendcollege is higher.     Fail to reject thenull hypothesis, there is sufficient evidence that the meanpercentage of young adults who attend college is higher.Reject thenull hypothesis, there is insufficient evidence that the meanpercentage of young adults who attend college is higher.