Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in more than 318 seconds. For a sample of 45 patients, the mean time in which the medicine relieved pain was 323 seconds. Assume the population variance is known to be 324. Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

To Test :-

H0 :- µ = 318
H1 :- µ ≠ 318

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 323 - 318 ) / ( 18 / √( 45 ))
Z = 1.8634

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Critical value Z(α) = Z(0.05) = 1.645
Z > Z(α) = 1.8634 > 1.645
Result :- Reject null hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.05 level of significance
P value = P ( Z < 1.8634 )  = 0.0312 ( From Z table )
Since 0.0312 < 0.05 ,hence we reject null hypothesis
Result :- Reject null hypothesis

P value = P ( Z < 1.8634 )  = 0.0312