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

Question

You are testing the null hypothesis that mu = 0 versus the alternative mu > 0 using alpha = .05. Assume sigma = 18. Suppose x^bar = 4.5 and n = 11 Calculate the test statistic and its P-value. Repeat assuming the same value of x^bar but with n = 21. Do the same for sample sizes of 31, 41, and 51 (Round the test statistic to two decimal places. Round the P-value to four decimal places.) value n = 11: z _____ P-value ______ n = 21: z ______ P-value n = 31: z ______ P-value n 41: z ______ P-value n = 51: z ______ P-value 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.

Explanation / Answer

from above we know that it is right tailed test

std error =std deviaiton/(n)1/2

hence z=(X-mean)/std error

and from above test stat we can calculate p value

hence

as sample size increases a test becomes more significant

n z P 11 0.8292 0.2035 21 1.1456 0.1260 31 1.3919 0.0820 41 1.6008 0.0547 51 1.7854 0.0371

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