Question

It is claimed that a new treatment is more effective than the standard treatment for prolonging the
lives of terminal cancer patients. The standard treatment has been in use for a long time, and from
records in medical journals, the mean survival period is known to be 4.2 years. The new treatment
is administered to 80 patients and their duration of survival recorded. The sample mean and the
standard deviation are found to be 4.5 and 1.1 years, respectively. Answer the following questions.
(a) Define µ in the context of the problem and formulate the null and alternative hypotheses.
(b) State the Type I and Type II errors for this problem and tell why Type I error is more serious.
(c) State the Z-test statistic for this problem and tell its distribution.
(d) Is the small, large or both small and large value of the Z-test statistic that will lead us to reject
the null hypothesis?
(e) Suppose the significance level is 0.05. Determine the critical value for the rejection region and
write down the decision rule.
(f) Calculate the value of Z-test statistic from the available data.
(g) Determine whether or not the null hypothesis is rejected at the significance level and tell why.
(h) Calculate the P-value and do the hypothesis testing based on the P-value.
(i) Express the conclusion in the context of the problem, using common English.

Answer 1