Sample Questions for Exam 2

Note - there are more questions in this sample than there will be in the real exam

Test significance at alpha = 0.05 unless otherwise indicated.

1. Using the data below, calculate the following confidence intervals.

   Data: 6.4, 8.1, 5.9, 6.9

1. The 95% CI
   
   
   
   
   
2. The 99.9% CI
   
   
   
   
   
3. The 95% CI if the sample size was increased by one but the mean and variance stayed the same.
   
   
   
   
   
   
2. You want to determine whether a certain hormone affects growth rates in mammals. Using mice as a model organism, you take two siblings from each of 6 litters of mice, and in each case inject one sibling with the hormone and the other with a placebo. You then weigh the mice two weeks later. The resulting data are below.
   

   Litter	Hormone	Placebo
   A	3.6	5.2
   B	3.6	5.5
   C	4.4	4.0
   D	3.7	4.6
   E	4.8	5.3
   F	3.6	3.8

   1. Perform an appropriate test, being sure to show your work.
      
      
      
      
      
      
      
      
   2. What type of error (type I or II) might you have made above? Explain.
      
      
      
      
      
      
3. What are the assumptions of the ANOVA test? That is, what conditions are the data supposed to meet?
   
   
   
   
   
   
   
4. You are investigating the general effects of smoking on physical activity capacity. You round up 9 nonsmokers, 9 moderate smokers and 9 heavy smokers as test subjects. You then choose three tests of activity capacity – bicycle ergometer, treadmill and step – and assign three people from each category to each test. The data obtained from the tests are the minutes until the subject becomes exhausted (data below).

   	Bicycle	Treadmill	Step
   Nonsmokers	12.8 13.5 11.2	16.2 18.1 17.8	22.6 19.3 18.9
   Moderate smokers	10.9 11.1 9.8	15.5 13.8 16.2	20.1 21.0 15.9
   Heavy smokers	8.7 9.2 7.5	14.7 13.2 8.1	16.2 16.1 17.8

   1. What type of test would you run on these data?
      
      
      
      
   2. Is each factor fixed or random?
      
      
      
      
   3. What are the results of the statistical test you ran, and what do you conclude from them?
      
      
      
      
      
      
      
      
      
      
      
5. Four strains of lab mice are being bred for increased litter size. The litter size of eight dams (mothers) of each breed is determined – see the sheet “Mice” in the Excel file.
    
   1. Carry out an ANOVA comparing the four breeds using these data. Find the resulting P value as closely as possible using Zar’s table B.4.
      
      
      
      
      
      
   2. If appropriate given the results in “a,” run a suitable post-hoc test to see which breeds differ in litter size. Use P = 0.05 as the critical value.
      
      
      
      
      
      
      
      
6. The good people at Kaplan commission a study to determine whether or not their courses really help students do better on the MCAT. They obtain MCAT scores from students who did and did not take their course at three different universities (data in Excel worksheet). Conduct an appropriate analysis of these data “by hand” (in Excel), summarize the results (below or in Excel) and interpret your results (below).
   
   
   
   
   
   
   
   
   
   
   
   
   
7. In a study of effective yet legal stimulants, a group of 10 students is each given one of four beverages to drink at midnight and then takes a word recall test at 2:00 am. The process is repeated for four nights, with each person receiving a different beverage each night in a random order. Analyze the resulting data (see Excel worksheet) using a repeated measures ANOVA. If difference among beverages are found, run post-hoc tests to determine which beverages are different from which. Describe your findings below.