A recent study from the University of Virginia looked at the effectiveness of an online sleep therapy program in treating insomnia. They took 45 random adults who suffered from insomnia. 22 of them were randomly selected to participate in the therapy program while the remaining 23 served as a control group. They scored each individual using an Insomnia Severity Index, and hoped to prove that participants in the program would have a lower score. For the 22 subjects who participated in the program, the average score was 6.59, with a standard deviation of 4.10. For the 23 subjects in the control group, the average score was 15.50, with a standard deviation of 5.34. a) State your null and tnaive hypotheses
b) Find the appropriate test statistic. t ((6.59 - 15.50) - 0) / sqrt( 4.10 2/225.34 2/23)-6.294
c) Find the p-value. Df-41 (use 40 on table) Outside the range of the table. P-value is very close to 0
d) If we are testing at the 0.05 significance level, what do you conclude? We reject the null hypothesis. There is evidence the program is effective
e) Is this an enumerative or an analytic study? This is an analytic study - we cannot list out the entire population of interest (all adults who suffer from insomnia). We did not cover this, but it is useful to think about.