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 325 seconds. For a sample of 54 patients, the mean time in which the medicine relieved pain was 333 seconds. Assume the variance is known to be 441.

Step 1 of 5:

Enter the hypotheses:

Step 2 of 5:

Enter the value of the z test statistic. Round your answer to two decimal places.

Step 3 of 5:

Specify if the test is one-tailed or two-tailed.

Step 4 of 5:

Enter the decision rule.

Step 5 of 5:

Enter the conclusion.

Answer 1

Step 1

H0 :- µ = 325
H1 :- µ > 325

Step 2

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 333 - 325 ) / ( 21 / √( 54 ))
Z = 2.80

Step 3

Since the alternative hypothesis is greater than ( > ), hence it is one tailed test.

Step 4

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Critical value Z(α) = Z(0.05) = 1.645
Z > Z(α) = 2.7994 > 1.645
Result :- Reject null hypothesis

Step 5

There is sufficient evidence to support the claim that the medicine relieves pain in more than 325 seconds.