Suppose you were asked to analyze each of the situations described below. (NOTE: DO NOT
DO THESE PROBLEMS!) For each, indicate which inference procedure you would use (from the list), the test statistic (
z,
t, or χ
2 ), and, if
t or χ
2 , the number of degrees of freedom.
a. Doctors offer small candies to sixty teenagers, recording the number of candies consumed by each. One hour later they test the blood sugar level for each person. Is there any evidence that high blood sugar levels in teenagers are related to the amount of candy eaten?
b. Which takes less time to travel to work –– car or train? We select a random sample of 45 businessmen and compare their travel time to work for both types of commute.
c. An orthodontist wonders if soda in the diet may be a factor in loose cement on children's braces. She checks the cement bonds of 40 randomly selected patients who do not drink soda, and 40 patients who do drink soda.
d. Forty people complaining of allergies take an antihistamine. They report that their discomfort subsided in an average of 18 minutes; the standard deviation was 4 minutes. The manufacturer wants a 95% confidence interval for the "relief time".
e. A health professional selected a random sample of 100 patients from each of four major hospital emergency rooms to see if the primary reasons for emergency room visits are similar in all four major hospitals. The primary reasons were categorized as accident, illegal activity, illness, or other.
f. A policeman believes that more than 40% of older drivers speed on highways, but a confidential survey found that 49 of 88 randomly selected older drivers admitted speeding on highways at least once. Is this strong evidence that the policeman was wrong?
g. According to United Nations Population Division, the age distribution of the Commonwealth of Australia is: 21% less than 15 years of age, 67% between 15 and 65 years of age, and 12% are over 65 years old. A random sample of 210 residents of Canberra revealed 40 were less than 15 years of age, 145 were between 15 and 65 years of age, and 25 were over 65 years old. Are the ages of Canberra residents unusual in any way?
h. Among a random sample of college-age students, 6% of the 473 men said they had been adopted, compared to only 4% of the 552 women. Does this indicate a significant difference between adoption rates of males and females in college-age students?
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