Exercise 9.3: Consider the following hypothesis test Ho: 22 Ha: > 22 A sample of

Question

Exercise 9.3: Consider the following hypothesis test Ho: 22 Ha: > 22 A sample of 75 is usedand the population standard deviation 1s 10. Use the critical value approach to state your conclusion for each of the sample result. Use -005. b, x=25 Hypothesis Test Step 1: State Ho, Ha Step 2: Specify level of significant Step 3: Compute Test statistic z =z-1-16- Use z-Test for Mean when is known Siep 4: Find the critical value and rejection nule The critical value = Rejection rule: Step 5.1: Determine whether to reject Ho Step 5.2: Write your conclusion in complete sentences

Explanation / Answer

a) xbar = 23
Below are the null and alternate hypothesis
H0: mu <= 22
Ha: mu > 22

Level of significance = 0.05

Test statistics, z = (23 - 22)/(10/sqrt(75)) = 0.8660

The critical = 1.65

Rejection rule: reject null hypothesis if calculated value of test statistics is greater than critical value of 1.65.

Do not reject H0

There is not significant evidence to conclude that sample mean is greater than 22.

b)
xbar = 25

Below are the null and alternate hypothesis
H0: mu <= 22
Ha: mu > 22

Level of significance = 0.05

Test statistics, z = (25 - 22)/(10/sqrt(75)) = 2.5981

The critical = 1.65

Rejection rule: reject null hypothesis if calculated value of test statistics is greater than critical value of 1.65.

Reject H0

There is significant evidence to conclude that sample mean is greater than 22.

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