Question

A researcher would like to evaluate the effect of a new cold medication on reaction time. It is known that under regular circumstances the distribution of reaction times is normal with µ = 200. A sample of n = 9 participants is obtained. Each person is given the new cold medication, and 1 hour later reaction time is measured for each individual. The average reaction time for this sample is M = 206 with SS = 648. The researcher would like to use a hypothesis test with ? = .05. to evaluate the effect of the medication. For the one-tailed test, assume that the medication is expected to increase reaction time.

1) State the hypothesis for a one-tailed and a two-tailed test.

2) Locate the critical region for a one-tailed and a two-tailed test.

3) Calculate the test statistic (the t statistic)

4) What is the decision for a one-tailed test? What is the decision for a two-tailed test?

5) Calculate the effect size estimating Cohen’s d and also r2. Briefly, describe what the effect sizes each mean.

Answer 1

We are given,

Then, the sample standard deviation is

1) For a one-tailed test

For a two-tailed test.

2)   For a one-tailed test, the local critical region of t₈-distribution at is 1.860.

and for a two-tailed test, the local critical region of t₈-distribution at are -2.306 and 2.306.

3) The test statistics is given by

Hence, assuming H₀ is true, the test statistics is

4) For one tailed test

As the test statistics is greater than the critical value, Hence we have sufficient evidence to reject H₀

Hence, we do not have sufficient evidence to conclude that the medication will increase the reaction time.

For two tailed test

As the test statistics between the critical value, hence we do not have have sufficient evidence to reject H₀.