Question

It is generally agreed that a certain standard treatment yields a mean survival period of 4.2 years for cancer patient. A new treatment is administered to 60 patients and their duration of survival is recorded. The sample mean and standard deviation of the duration is 4.5 years and 0.8 years, respectively. Does the new treatment increase the mean survival period? Choose the appropriate hypotheses to test the claim.

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 4.2 versus Ha: µ > 4.2

This is an upper tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 4.2

Xbar = 4.5

S = 0.8

n = 60

df = n – 1 = 59

α = 0.05

Critical value = 1.6711

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (4.5 - 4.2)/[0.8/sqrt(60)]

t = 2.9047

P-value = 0.0026

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the new treatment increase the mean survival period.