Question

# A sample of 37 observations is selected from a normal population. The sample mean is 25,...

A sample of 37 observations is selected from a normal population. The sample mean is 25, and the population standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level. H0 : μ ≤ 24 H1 : μ > 24 (a) Is this a one- or two-tailed test? "One-tailed"-the alternate hypothesis is greater than direction. "Two-tailed"-the alternate hypothesis is different from direction. (b) What is the decision rule? (Round your answer to 2 decimal places.) H0,when z > (c) What is the value of the test statistic? (Round your answer to 2 decimal places.) Value of the test statistic (d) What is your decision regarding H0? Reject Do not reject There is evidence to conclude that the population mean is greater than 24. (e) What is the p-value? (Round your answer to 4 decimal places.) p-value

a)

This is one tailed test.

b)

Critical value at 0.05 level = 1.645

Decision rule - Reject H0 if test statistics z > 1.645

c)

Test statistics

z = - / / sqrt(n)

= 25 - 24 / 5 / sqrt(37)

= 1.22

d)

Since test statistics falls in non-rejection region, do not reject H0.

There is insufficient evidence to conclude that the population mean is greater than 24.

e)

p-value = P( Z > z)

= P( Z > 1.22 )

= 0.1112 (From Z table)

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