Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 334 seconds. For a sample of 86 patients, the mean time in which the medicine relieved pain was 341 seconds. Assume the variance is known to be 529.

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.

Reject H0 if z> _______

Step 5 of 5: Enter the conclusion.

a. Reject Null Hypothesis

b. Fail to Reject Null Hypothesis

Answer 1

Solution :

= 334

= 341

= 529 = 23

n = 86

This is the right tailed test .

The null and alternative hypothesis is

H₀ :   = 334

H_a : > 334

Test statistic = z

= ( - ) / / n

= (341 -334) /23 / 86

= 2.82

p(Z >2.82 ) = 1-P (Z < 2.82 ) = 0.0024

P-value = 0.0024

= 0.02  

This is a one tailed test

The critical value for a right-tailed test is z_c​=2.05.

The rejection region for this right-tailed test is R ( z:z>2.05)

z=2.822>z_c​=2.05

0.0024 < 0.02

Reject the null hypothesis .