Question

The current median survival time of patients  with acute myelogenous lukemia who achieve complete remission from conventional treatment is 21 months. A new procedure is being studied. Researchers hoped that with this new procedure, the median survival time will be improved. The following is the survival time for 10 patients who received the new treatment:

Patient: 1,2,3,4,5,6,7,8,9,10

Survival Time: 24.1, 25.8, 20.5, 20.9, 27.3, 21.5, 20.1, 28.9, 19.2, 26.3

A) Let M be the median survival time for patients under the new treatment. What is the appropriate alternative hypothesis?

B) Find the p-value of the Sign Test for the appropriate hypotheses.

C) Find the value of the Wilcoxon Signed-Rank test statistic for the appropriate hypotheses

Answer 1

A) Let M be the median survival time for patients under the new treatment. What is the appropriate alternative hypothesis?

Ans:

B)

## Using R-software
install.packages("EnvStats") ## Install this R package

library(EnvStats)

Time=c(24.1, 25.8, 20.5, 20.9, 27.3, 21.5, 20.1, 28.9, 19.2, 26.3)

signTest(x=Time, mu = 21, alternative = "greater")

The p-value of the Sign Test is 0.377 and greater than the 0.05 level of significance. Hence, we can not reject the null hypothesis and conclude that the new procedure does not help to improve the median survival time.

## C)

The value of the Wilcoxon Signed-Rank test statistic is 42.5 and the corresponding p-value is 0.06958. This p-value is greater than 0.05 level of significance. Hence, we can not reject the null hypothesis and conclude that the new procedure does not help to improve the median survival time.