Discuss the below:
In the following exercises we consider using a random sample of 100 measurements to test null hypothesis: u=80 versus alternative hypothesis: u>80
Q1 If mean x =85 and standard deviation =20, calculate the value of the test statistic z.
Q2 Use a rejection point to test null hypothesis versus alternate hypothesis by setting probability of Type I error equal to .05
Q3 Use a rejection point to test null hypothesis versus alternate hypothesis by setting probability of Type I error equal to .001
Q4 Suppose that a random sample of nine measurements from a normally distributed population gives a sample mean of x = 2.57 and a sample standard deviation of s = .3. Use rejection points to test null hypothesis : u= 3 versus alternate hypothesis: u does not equal 3 using levels of significance a= .10, a=.05, a=.01, and a=.001. What do you conclude at each value of a?