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Chapter 10: Q.4 (page 662)

Men versus women The National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey interviewed a random sample of 1917people 21to 25years old. The sample contained 840men and 1077women. 49The mean and standard deviation of scores on the NAEP's test of quantitative skills were x炉1=272.40and s1=59.2for the men in the sample. For the women, the results were x炉2=274.73and s2=57.5. Is the difference between the mean scores for men and women significant at the 1% level? Give appropriate statistical evidence to justify your answer.

Short Answer

Expert verified

No, there is not enough proof to help the claim that there is a difference.

Step by step solution

01

Given Information

x炉1=272.40

x炉2=274.73

s1=59.2

s2=57.5

n1=840

n2=1077

02

Explanation

The hypothesis

H0:渭1=渭2

H1:渭1鈮�渭2

The test statistic:

t=x炉1-x炉2s12n1+s22n1

=272.40-274.7259.22840+57.521077

=-0.866

03

Explanation

The degrees of freedom:

df=minn1-1,n2-1

=min(840-1,1077-1)

=839>100

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme.

localid="1650369677218" 0.30=2脳0.15<P<2脳0.20

=0.40

localid="1650352701568" 0.30<P<0.40

The P-value is the chance of getting the test statistic's result, or a number that is more severe.

P>0.01=1%鈬�Fail to rejectH0

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