Question

In: Statistics and Probability

The director of research and development is testing a new drug. She wants to know if...

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.05 level that the drug stays in the system for more than 375 minutes. For a sample of 38 patients, the mean time the drug stayed in the system was 382 minutes. Assume the population standard deviation is 24.

Step 1 of 6 : State the null and alternative hypotheses.

  

Step 2 of 6 Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6 : Specify if the test is one-tailed or two-tailed.

Step 4 of 6 : Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6 : Identify the level of significance for the hypothesis test.

Step 6 of 6 : Make the decision to reject or fail to reject the null hypothesis.

Solutions

Expert Solution

We have to test, if the drug stays in the system for more than 375 minutes i.e.,

.....................(step 1)

Given, the sample size, n = 38

sample mean, = 382(minutes)

population standard deviation, = 24.

test statistic:

............................(step 2)

The test is a one tailed test. ....................................(step 3)

for this testing, p-value of the test statistic z is P(Z > 1.80) = 0.0359. .........................(step 4)

Using the significance level of 0.05, ..............................(step 5)

decision rule: ...............................(step 6)

we reject the null hypothesis if value of z is greater than Z0.05 = 1.645 (value from standard normal table) or if p-value < 0.05.

Since, z = 1.80 > 1.645 and also p-value=0.0359 < 0.05, we reject the null hypothesis at 0.05 level of significance.


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