A random sample of 64 observations produced the following summary statistics: x-

Question

A random sample of 64 observations produced the following summary statistics:

x-bar = 35.45

s2 = 3.4

A) In a test of null hypothesis H0: = 36 and Ha: < 36 test statistics was found to be z = -2.39. With a level of significance = 0.01 what is your decision about this hypothesis test? Justify your answer with the help of p-value.

B) In part A if the test becomes a two-tailed test, H0: = 36 and Ha: 36 with the same test statistic z = -2.39. What would be the p-value of this hypothesis test? At = 0.01 what would be your statistical decision?

Explanation / Answer

A)

p value(One tailed) for the test statistics -2.39 is 0.0084.

At 0.01 level, since p value < 0.01 level, we have sufficient evidence to reject H0.

We conclude that, Reject H0 and we have enough evidence to support the claim.

B)

p value(Two tailed) for the test statistics -2.39 is 0.0168.

At 0.01 level, since p value > 0.01 level, we do not have sufficient evidence to reject H0.

We conclude that, Do not reject H0 at 0.01 level.

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