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Name: ______________________________
Stat 302H Final Exam May 8, 2006
Instructions: You may use the tables in the back of the text. Some of the problems require only minimal calculations. In general, if you don’t have time to carry out the calculations, just substitute numbers into appropriate formulas.
- One of our class presentations addressed the continuing decline in the proportion of male birth in industrialized countries. Many suggest that exposure to certain industrial chemicals reduces the likelihood of male births. For example, there was a chemical plant explosion in Seveso, Italy, in 1977 which exposed workers to an industrial chemical DBCP. Of the exposed individuals, 12 had wives which gave birth and only 2 of these offspring were male. Hence the observed proportion of male births is 0.167. Is this sufficient evidence to conclude that a male offspring is less likely than a female offspring among exposed workers? Conduct a hypothesis test, give a p -value, and give a concise statistical interpretation of your results in the context of the problem.
Hypothesis Test:
p -value:
Conclusion:
- An experiment was conducted to compare the weights of the combs of roosters fed two different vitamin-supplemented diets. Twenty-eight healthy roosters were randomly divided into two groups, with one group receiving diet I and the other receiving diet II. After the study period the comb weight (in milligrams) was recorded for each rooster. The data are:
Diet I 73 130 115 144 127 126 112 76 68 101 126 49 110 123 Diet II 80 72 73 60 55 74 67 89 75 66 93 75 68 76
a) Suppose you wanted to conduct a nonparametric test to compare these data. Using α = .05, complete the following:
H 0 :
Ha : (two-sided):
Value of test statistic:
p -value:
Conclusion:
- Suppose that in the past, a rooster with a comb weight exceeding 100 would be unusual. However, with Diet I the mean weight is x = 105.7with standard deviation 28.3.
a) Test whether you have evidence the Diet I produces roosters with a mean comb
weight exceeding 100, using a population standard deviation of 30 and α = .05.
H 0 :
Ha :
value of test statistic:
p -value:
conclusion:
b) Find the power of the above test to detect an increase of 5mg in the population mean weight, i.e. to reject H 0 if the true population mean were 105 mg.
- The shelf life of packaged food depends on many factors. Dry cereal is considered to be a moisture-sensitive product (no one likes soggy cereal!), with the shelf life determined primarily by moisture content. In a study of the shelf life of one particular brand of cereal, x = time on shelf (stored at 73oF and 50% relative humidity) and y = moisture content were recorded. The resulting data from n = 14 trials are from “Computer Simulation Speeds Shelf Life Assessments” ( Package Engr. (1983): 72-73).
time moisture time moisture 0 2.8 20 3. 3 3.0 24 3. 6 3.1 27 4. 8 3.2 30 4. 10 3.4 34 4. 13 3.4 37 4. 16 3.5 41 4.
Some summary quantities are:
2 2
x y x x y y x x y y
The SPSS scatterplot of data is:
c) Find a 95% interval for the moisture content of an individual box of cereal that has been on the shelf 30 days.
d) Suppose that the data actually comes from 2 manufacturers, with every odd numbered sample from company A and every even one from company B. Suppose one uses an indicator variable, say
0 for company A 1 for company B x =
Discuss how one could test whether company A and B have equal slopes. Give the model and show what you would test.
e) Assuming the slopes are equal for companies A and B, show how to test whether they have identical regression lines. Give the model, and show what you would test.
