A random sample of 10 observations was drawn from a large normally distributed p

Question

A random sample of 10 observations was drawn from a large normally distributed population. The data is below. 19 15 18 20 17 13 11 19 13 17 Test to determine if we can infer at the 1 % significance level that the population mean is not equal to 15, filling in the requested information below. A. The value of the standardized test statistic: -1.1456 B. The rejection region for the standardized test statistic: (-infty, - 2.9768)U(2.9768, infty) C. The p-value is 0.271167 D. Your decision for the hypothesis test: A. Reject H_0. B. Do Not Reject H_1. C. Reject H_1. D. Do Not Reject H_0.

Explanation / Answer

Below are the null and alternate hypothesis

H0: mu = 15

H1: mu not equals to 15

From the given data, we have

mean = 16.2

std. dev. = 3.0478

SE = 0.9638

(A) Value of test statistics, z = (15 - 16.2)/0.9638 = -1.2451

(B) For 1% Significance level, z-value = 2.576

a = mean - z*SE = 16.2 - 2.576*0.9638 = 13.7173

b = mean + z*SE = 16.2 + 2.576*0.9638 = 18.6828

Hence the rejection region is (-infy, 13.7173) U (18.6828, +infy)

Note: these values will be slightly different if we use t-statistics t-value = 3.25

a = mean - t*SE = 16.2 - 3.25*0.9638 = 13.07

b = mean + t*SE = 16.2 + 3.25*0.9638 = 19.33

Hence the rejection region is (-infy, 13.07) U (19.33, +infy)

(c)

p-value = 0.2131 (using z - table)

p-value = 0.2445 ( using t -table)

(D)

As p-value is greater than significance level of 0.01, faile to reject null hypothesis i.e. do not reject H0 (Option D)

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