1. A random sample of N = 25 individuals is selected from a population, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be X = 35.2 with SS = 412. Construct a 95% confidence interval for , the population mean for the treatment group.

2. To evaluate the effect of a treatment, a sample is obtained and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be X = 14.8 with a standard deviation of = 4.1. Construct a 95% confidence interval for , the population mean for the treatment group, assuming the sample contains: (a) N = 15 individuals. (b) N = 30 individuals. (c) Comparing your answers for parts (a) and (b), how does the size of the sample influence the width of your confidence interval for ?

3. A researcher surveys a group of college students to determine the negative life events that they experienced in the past 5 years and their current feeling of well-being. For N = 18 participants with 2 or fewer negative experiences, the average well-being score was X = 42 with SS = 398. For the N = 16 participants with 5 to 10 negative experiences the average score is X = 48.6 with SS = 370. Construct a 95% confidence interval for the difference between the population means for the two groups. 4. In 1974, Loftus and Palmer conducted a classic study demonstrating how the language used to ask a question can influence eyewitness memory. In the study, college students watched a film of an automobile accident and then they were asked questions about what they saw. One group was asked "About how fast were the cars going when they smashed into each other?" Another group was asked the same question except the verb was changed to "hit" instead of "smashed into". The "smashed into" group reported significantly higher estimates of speed than the "hit" group. Suppose a researcher repeats the study with a sample of today's college students and obtains the following results:

Smash into. Hits

n=15 n=15

x=40.8 X=34.0

ss=510 ss=414