Question

The length of pain relief from the drug Tramadol is known to be normally distributed. The pharmaceutical company that makes Tramadol claims that the average pain relief lasts longer than 4 hours. A random sample of 15 patients on Tramadol had a mean of 4.28 hours and a standard deviation of 0.5 hours.

a) State the hypotheses

b) State the rejection region for 훼=0.025

c) Perform a Student’s T-test and state your conclusion.

d) The p-value for this sample will lie between which two values?

Answer 1

Solution :

= 4

= 4.28

S =0.5

n = 15

a ) This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 4

Ha : > 4

Test statistic = t

= ( - ) / S / n

= (4.28-4) / 0.5 / 15

= 2.169

Test statistic = t = 2.169

b ) The significance level is α=0.025, and the critical value for a right-tailed test is tc​=2.145

c )  It is observed that t=2.169 > tc​=2.145, it is then concluded that the null hypothesis is rejected

d )P-value =0.0239

= 0.025  

P-value <

0.0239 < 0.025

Reject the null hypothesis .

There is sufficient evidence to suggest that