A General Social Survey asked respondents to rate themselves on a seven-point sc

Question

A General Social Survey asked respondents to rate themselves on a seven-point scale for political views with a 1 being extremely liberal and a 7 being extremely conservative. From the 4333 respondents in 2006, the mean response was 4.12 with a standard deviation of 1.41. Testing the hypotheses Ho: m = 4.0 versus H1: m 4.0 resulted in a p-value of 0.00000002, providing extremely strong evidence that the true mean differs from 4.0. Suppose the sample mean of 4.12 and sample standard deviation of 1.41 were from a sample size of only 25, rather than 4333.

a. Find the test statistic.

b. Find the p-value for testing Ho: m = 4.0 versus H1: m 4.0. Interpret the result.

c. Explain what this illustrates about the effect of sample size on the size of the p-value. How does this relate to practical significance?

Explanation / Answer

a. Find the test statistic.

t = ( 4.12 - 4.0 ) / ( 1.41 / srfqt 4333 )

t = 5.602

p value : 0.0000002

since p value is lower than signifincace level

we reject Ho

conclusion

mean is different form 4.0

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