Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.01 level that the medicine relieves pain in more than 313 seconds. For a sample of 34 patients, the mean time in which the medicine relieved pain was 320 seconds. Assume the standard deviation is known to be 24.

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

Solution :

Given that,

Step 1 of 5:

The null and alternative hypothesis is,  

Ho: 313

Ha: 313

Step 2 of 5:

The test statistics,

Z =( - )/ (/n)

= ( 320 - 313 ) / ( 24 / 34 )

= 1.70

Step 3 of 5:

This a right (One) tailed test.

Step 4 of 5:

Critical value of  the significance level is α = 0.01, and the critical value for a right-tailed test is

= 2.33

Rejection region is z > 2.33

Since it is observed that z = 1.70 < = 2.33, it is then concluded that the null hypothesis is fail to reject.

Step 5 of 5:

If there is no evidence at the 0.01 level that the medicine relieves pain in more than 313 seconds.