Suppose you have the following null and alternative hypotheses: H0: = 200 and H1

Question

Suppose you have the following null and alternative hypotheses: H0: = 200 and H1: 200. You collect a sample of data from a population that is normally distributed and the population standard deviation is unknown. The sample size is 25, the sample mean is 190, and the sample standard deviation is 15. At a level of significance of 0.05, what is your conclusion:

A: Do not reject H0 since the test statistic is greater than the critical value.

B: Reject H0 since the test statistic is between the critical values.

C: Do not reject H0 since the test statistic < the p-value.

D: Reject H0 since the test statistic is less than the critical value.

Explanation / Answer

t = ( 190 - 200 ) / ( 15 / srqt 25 )

t = -3.33

for alpha / 2 = 0.025 df = 24 critical value : +/- 2.064

since t < critical value we reject Ho

D: Reject H0 since the test statistic is less than the critical value.

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