Question

1. To determine whether a new drug is useful for people that suffer from obsessive compulsive disorder (OCD), you obtain a random sample of n = 100 patients with OCD. You are particularly interested in the “checking” type of OCD. Checkers are compelled to engage in ritualistic behaviors such as checking the gas on the stove before they leave the house or making sure the doors and windows are locked before bedtime. Some checkers are so compelled by their obsessions that they repeat the checking behavior hundreds of times a day which can severely impact the quality of life. Prior to any experimentation, you ask the participants to monitor their behaviors closely and self-report the frequency of compulsive checking behaviors for two weeks. From the initial self-reports, you have determined that average baseline frequency of the compulsive rituals is  = 135 times per day with a standard deviation of σ = 40. You have reason to believe that the ritualistic behaviors should decrease so you choose a one-tailed test and the standard alpha level of 0.05. Participants will continue self-reporting compulsive ritualistic behaviors. In addition, half will take the active drug for two weeks and the other half will get the placebo. Participants will not know which drug they are getting, the active drug or placebo. After two weeks, the groups will switch medications and continue for two more weeks. At the end of a month, you determine from the self-reports that compulsive ritualistic behaviors declined when participants were taking the active medication to a new mean of M = 127. But was the change large enough to claim statistical significance? Complete this example showing your work by providing answers to the questions at each blank. Finally, using a z-test determine whether there is a significant decrease in the frequency of compulsive rituals after taking the drug for several weeks. What is the appropriate conclusion/decision?

State the null and alternative hypothesis
H₀: ________________________
H₁: ________________________

\

Figure 1: z-test formula
μ = 135 M = 127
σ= 40 n = 100

Using the data provided determine the frequency of ritualistic behaviors per day
Mean _____________________ Standard deviation _______________
Estimated standard error ______________ z-test statistic _________________
With alpha at 0.05

The critical value of one-tailed Z_crit= +/- 1.65

Observed value of z_obs _____________
a. Fail to reject H₀ b. Reject H₀

Answer 1