Discuss the below:
Q1. To test the null hypothesis that the average lifetime for a particular brand of bulb is 750 hours versus the alternative that the average lifetime is different from 750 hours, a sample of 75 bulbs is used. If the standard deviation is 50 hours and α is equal to 0.01, what values for x‾ will result in rejection of the null hypothesis.
Q2. Describe the action that would result in a type I error and a type II error if each of the following null hypotheses were tested.
a. H0: There is no waste in US Defense Department spending
b. H0: This fast-food menu is not low fat
Q3. Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:
a. H0: μ = 25 and Ha: μ≠ 25, α = 0.10
b. H0: μ ≤ 32 and Ha: μ > 32, α = 0.01
c. H0: μ ≥ 13 and Ha: μ < 13, α = 0.05