You are testing the null hypothesis that = 0 versus the alternative > 0 using =

Question

You are testing the null hypothesis that = 0 versus the alternative > 0 using = .05. Assume = 21. Suppose x = 5 and n = 14. Calculate the test statistic and its P-value. Repeat assuming the same value of x but with n = 24. Do the same for sample sizes of 34, 44, and 54. (Round the test statistic to two decimal places. Round the P-value to four decimal places.)

Plot the values of the test statistics versus the sample size. Do the same for the P-values. (Do this on paper. Your instructor may ask you to turn this in.) Summarize what this demonstration shows about the effect of the sample size on significance testing.

As sample size increases, a test becomes more significant.

As sample size increases, a test becomes less significant.   

As sample size increases, there is no effect on the significance.

As sample size decreases, a test becomes more significant.

n = 14: z ___ P-value ___ n = 24: z ___ P-value ___ n = 34: z ___ P-value ___ n = 44: z ___ P-value ___ n = 54: z ___ P-value ___

Explanation / Answer

For n=14, z=x-mu/(sd/sqrt(n))=5-0/21/sqrt(14))=0.89 So p value=0.1867

For n=24, z=1.17, p value=0.1210

For n=34, z=1.39, p value=0.0823

For n=44, z=1.58, p value=0.0571

For n=54, z=1.75, p value=0.0401

As sample size increases p value decreases so the result is not significant at p < 0.05.

As sample size increases, a test becomes less significant.   

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