1. What is the probability of rolling a four in the gambling dice game of craps (given two six sided dice)? What is the probability that a player can roll a four 3 times in a row (assume that rolling the dice each time does not affect the outcome of the next roll)?
2. Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is picked from population A, and random sample of 50 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why?
3. Suppose we obtained data on vein size after application of a nitroglycerin ointment in a sample of 50 patients. The mean vein size is found to be 8.7mm with an SD of 2.1. Using a t distribution table, what are the confidence limits for a 95% confidence interval? For a 99% confidence interval?
4. In a pilot study evaluating the use of a new drug to lower resting heart rates (HR) of patients, the following data was recorded:
5. Write one or two sentences that could be used to report the results obtained for the t-test in Exercise 4.
6. For which of the following situations is the independent groups t-test appropriate (if inappropriate, why?):
7. For which of the following situations is the dependent groups t-test appropriate (if not appropriate, why?)
8. Suppose we wanted to test the hypothesis that a control group of cancer patients (Group 1) would report higher mean pain ratings than an experimental group receiving special massage treatments (Group 2). Use the following information. Compute a t-statistic for independent groups:
9. Write one or two sentences that could be used to report the results obtained for the t-test in Exercise 8.
10. For each of the following t values, indicate whether the t is statistically significant for a two-tailed test, at the specified alphas:
11. For each of the following situations, indicate whether ANOVA is appropriate; if not appropriate, the reason why not; and, if appropriate, the type of ANOVA that would be used (i.e., one-way, repeated measures, etc.)
12. Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Scale or PSS) of three groups of people: non-smokers, smokers, and people who recently quit smoking. Using the following data for PSS, do a one-way ANOVA to test the hypothesis that the population means are equal:
13. A new motorcycle is being developed to meet new gas mileage standards recently passed by the federal government. An engineer tested three model designs by randomly assigning the motorcycles in a blind study (the riders recorded the mileage but did not know the design of the motorcycle, only its code). The data in miles per gallon (MPG) for the three designs is listed below:
14. For each of the following F values, indicate whether the F is statistically significant at the specified alpha level: