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 = 18. Suppose x = 5.1 and n = 13. Calculate the test statistic and its P-value. Repeat assuming the same value of x but with n = 23. Do the same for sample sizes of 33, 43, and 53. (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 = 13: z P-value n = 23: z P-value n = 33: z P-value n = 43: z P-value n = 53: z P-value

Explanation / Answer

From the given data

Correct Answer: As sample size increases, a test becomes more significant.

n = 13: z 1.0216 P-value 0.1535 n = 23: z 1.3588 P-value 0.0871 n = 33: z 1.6276 P-value 0.0518 n = 43: z 1.8579 P-value 0.0316 n = 53: z 2.0627 P-value 0.0196

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