1. In a study of brain waves during sleep, a sample of 29 college students were randomly separated into two groups. The first group had 15 people and were each given ½ liter of red wine before sleeping. The second group had 14 people and were given no alcohol before sleeping. All participants when to sleep at 11 PM and their brainwave activity was measured from 4-6 AM. The group drinking alcohol had a mean brainwave activity of 19.65 hertz and a standard deviation of 1.86 hertz. The group not drinking alcohol had a mean of 6.59 hertz and standard deviation of 1.91 hertz. Compute a 90% confidence interval for the difference in population means of groups drinking alcohol before sleeping and those not drinking alcohol before sleeping. Explain the meaning of the confidence interval.
2. A study comparing children's reading age (in months) was developed using identical twin toddlers. One set of 6 twins played for 2 hours each day with educational toys (experimental group), the corresponding set of 6 twins played for 2 hours each day with non-educational toys (control group). The mean difference in reading age between the experimental group and control group of 6 sets of twins was -2.33 months and the standard deviation of the sample difference was 2.16 months. Set up a hypothesis test to determine if there is a difference between the 2 groups and use the appropriate sample test statistic to determine if the difference in reading age is significant at the 5% level.
3. Discuss the following:
a. What type of data can be examined using the Chi-Squared Te
b. What is the only constraint in using Chi-Squared Tests?
c. What problems can be caused by the way the data have been grouped?