Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.025 level that the medicine relieves pain in more than 318 seconds. For a sample of 7 patients, the average time in which the medicine relieved pain was 324 seconds with a standard deviation of 23. Assume the population distribution is approximately normal.

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

Step 2 of 5: 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

Step 1: Here claim is that mean is more than 318 seconds

As we know null hypothesis always have equality sign, hypothesis are

vs

Step 2: As it is given that distribution is normal, test statistics is

Step 3: As alternative hypothesis is right tailed test, it is one tailed test

Step 4: The t-critical value for a right-tailed test, for a significance level of α=0.025 is

tc​=2.447

Graphically

So if t statistics >tcritical reject the null hypothesis

Step 5: Here we see that t statistics=0.69<tcritical=2.447

Hence we fail to reject the null hypothesis