Question

1. A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 minutes. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and a standard deviation of 42.3 minutes. Assume that the 16 sample values appear to be from a normally distributed population.

   1. a) Test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 minutes at the ? = 0.05 level of significance. Use the critical value method. (Show all six steps for hypothesis testing.)

   2. b) Explain what it would mean to make a Type I error.

   3. c) Explain what it would mean to make a Type II error.

Answer 1

a) STEP 1: NULL HYPOTHESIS H0: MINUTES

ALTERNATIVE HYPOTHESIS Ha: MINUTES

STEP 2: Level of significance=

STEP 3: Test statistic under null hypothesis H0 is

STEP 4: This is one tailed test . Critical Value under this is with degrees of freedom is -1.753.

STEP 5: Since Calculated value of t is GREATER than the CRITICAL VALUE of t therefore NOT SIGNIFICANT.

DECISION: DO NOT REJECT NULL HYPOTHESIS H0.

Step 6: Conclusion: We don't have sufficient evidence to conclude that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 minutes at the ? = 0.05 level of significance.

b) Type I error: REJECTING H0 WHEN IT IS TRUE. IN THIS CASE REJECTING H0 AND CONCLUDING THAT after treatment with zopiclone, subjects have a mean wake time of less than 102.8 minutes but actually there is no affect of treatment.

c) Type II error: Retaining H0 when Ha is true: It means Retaining Null hypothesis and concluding that there is no affect of treatment but actually there is affect of treatment.