Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.1 level that the medicine relieves pain in more than 346 seconds. For a sample of 16 patients, the average time in which the medicine relieved pain was 351 seconds with a variance of 529. Assume the population distribution is approximately normal.

Step 1 of 5: State the null and alternative hypotheses.

Step 2 Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5:

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

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5:

Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

Given that,

Population mean = = 346

Sample mean = = 351

Sample standard deviation = s = 18.73

Sample size = n = 16

Level of significance = = 0.1

1

The null and alternative hypothesis is,

Ho: 346

Ha: 346

2

The test statistics,

t = ( - )/ (s/)

= ( 351 - 346 ) / ( 18.73 / 16 )

= 1.068

3

This a right (One) tailed test

4

Critical value of  the significance level is α = 0.05, and the critical value for a right tailed test is

= 1.341

5

Since it is observed that, t = 1.068 < = 1.341, it is then concluded that the null hypothesis is fails to reject.