Fc 8 Data Sets Below: Thank You! 8. Chapter 10, Section 10.2, Problem 14 Aa Aa E

Question

Fc 8

Data Sets Below: Thank You!

8. Chapter 10, Section 10.2, Problem 14 Aa Aa 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 R 15.2% of the older adults had attended college. Large surveys of young adults (ages 25-34) were taken in n2 35 U.S. cities. The sample mean for these cities showed that R 19.7% of the young adults had attended college. From previous studies, it is known that 01 7.2% and 02 5.2% (Reference: American Generations by s. Mitchell) Does this information in that the population dicate mean percentage of young adults who attended college is higher? Use or 0.05 what is the level of significance? Level of significance

Explanation / Answer

Level of significance = 0.05

To test the hypothesis,

H0: 1 = 2 vs H1 : 1<2

You will use the standard normal distribution with df = 95 because sigma 1 and sigma 2 are known and the population distribution are normal.

X1bar - X2bar = 15.2 - 19.7 = -4.5

sigma1= 7.2 , sigma2 = 5.2 , n1= 32, n2 = 35

sample test statistic = (-4.5) / [(sigma1/sqrt(n1)+sigma2/sqrt(n2))]

test statistic = -4.5 / [(7.2/sqrt(32))+(5.2/sqrt(35))]

test statistic = -1.881

shaded area corresponding to the p value is A

p value = 0.0036 < 0.05

so we reject H0 at 5% los.

You reject the null hypothesis because p value < alpha

At the 5% los , the evidence is sufficient to show that the mean percentage who attended college is higher in the population of young adults than in the population of older adults.

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