Question

Please clearly show and label each step

1. Consider the following hypothesis test:

H_o: μ = 16

H₁: μ ≠ 16

A sample of 50 provided a sample mean of 15.15. The population standard deviation is 3.

1. Compute the value of the test statistic.

2. What is the p value?

3. At α = 0.05, what is the rejection rule using the critical value? What is your conclusion?

Answer 1

Solution:
Null hypothesis H0: mean = 16
Alternate hypothesis H1: mean is not equal 16
Population standard is given and sample size is greater than 30 so we will use Z test
Zstat = (15.15-16)/3/sqrt(50)
Zstat = -0.85/3/7.07 = -2.00
this is two tailed test so we can find p-value from z table so p-value is 0.0576
At alpha = 0.05, we are failed to reject the null hypothesis as p-value is greater than alpha value so we are failed to reject the null hypothesis.

At Zcritical value is +/- 1.645 if Ztest value is in between -1.645 to +1.645 than we will reject H0 else do not reject H0. Here we are failed to reject the null hypothesis.