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 = 14. Suppose x = 4.6 and n = 15. Calculate the test statistic and its P-value. Repeat assuming the same value of x but with n = 25. Do the same for sample sizes of 35, 45, and 55. (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 = 15: z P-value n = 25: z P-value n = 35: z P-value n = 45: z P-value n = 55: z P-value

Explanation / Answer

z=x-//n

n=15, z=4.6-0/14/15=1.27, p-value=0.1020

n=25, z=4.6-0/14/25=1.64, p-value=0.0505        

n=35, z=4.6-0/14/35=1.94, p-value=0.0262

n=45, z=4.6-0/14/45=2.20, p-value=0.0139

n=55, z=4.6-0/14/55=2.44, p-value=0.0073

We can see from the data above that as sample size is going up, p-value is going down. If the p-value is less than or equal to alpha (p< .05), then we reject the null hypothesis, and the result is considered statistically significant. If the p-value is greater than alpha (p > .05), then we fail to reject the null hypothesis, and the result is considered statistically insignificant. Hence, the correct answer is As sample size increases, a test becomes more significant.

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