Question: It has been claimed that the mean weight of women at a college is 54.4 kgs. Prof Hart doubts this statement and sets out to show that the mean weight is not 54.4 kg. To test the claim, he takes a random sample of 100 weights from among the women. A sample mean of \(53.75\) kg results. Is this sufficient evidence for the professor to reject the claim? Use alpha = .05 and sigma = 5.4 kg.

a. State the null and alternate hypotheses.
b. Calculate the z test statistic
c. Find the critical values and the critical regions
d. State the conclusion
e. state the p-value for this test