Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided

Question

Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided a sample mean of 14.17. The population standard deviation is 6. a. Compute the value of the test statistic (to 2 decimals). b. What is the p-value (to 4 decimals)? c. Using = .05, can it be concluded that the population mean is not equal to 15? Answer the next three questions using the critical value approach. d. Using = .05, what are the critical values for the test statistic? (+ or -) e. State the rejection rule: Reject H0 if z is the lower critical value and is the upper critical value. f. Can it be concluded that the population mean is not equal to 15?

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 15
HA : 15
Standard deviation = 6

Hypothesis test results:

Hence,

a) Test statistic = -0.98

b) p - Value = 0.328

c) No, it can't be concluded that population mean is not equal to 15 since p - value is greater than 0.05.

d) Critical values = -1.96, 1.96

e) Reject Ho if z < -1.96 and z > 1.96

f) No, it can't be concluded that population mean is not equal to 15 since test statistic does not lie in the rejection region.

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