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. A researcher wonders if meat in the diet may be a factor in high blood pressure. She compares the blood pressures of 40 randomly selected vegetarians, to those of 40 people who eat meat.
b. According to the American Red Cross, 45% of Americans have Type O blood, 40% Type A, 11% Type B, and 4% Type AB. Last week a blood drive at the high school collected 132 pints of blood. If 51 were Type O, 55 Type A, 17 Type B, and 9 were Type AB, was this yield unusual in any way?
c. Among a random sample of college-age drivers 5% of the 576 men said they had been ticketed for speeding during the past year, compared to only 3% of the 552 women. Does this indicate a significant difference between college males and females in terms of being ticketed for speeding?
d. Who is paid more in New York State - teachers or policemen? We select a random sample of 25 New York cities and find the starting salaries of teachers and policemen in each.
e. Researchers offer small cookies to nine nursery school children and record the number of cookies consumed by each. Forty-five minutes later they observe these children during recess, and rate each child for hyperactivity on a scale from 1 - 20. Is there any evidence that sugar contributes to hyperactivity in children?
f. 22 people complaining of indigestion take an antacid. They report that their discomfort subsided in an average of 13 minutes; the standard deviation was 4 minutes. The manufacturer wants a 95% confidence interval for the "relief time."
g. A sports fan selected a random sample of 100 games from each of the NBA, the NFL, the NHL, and Major League Baseball to see if overtimes (or extra innings) are equally likely to occur in all four sports.
h. A teacher believes that no more than 10% of high school students ever cheat on an exam, but a confidential survey found that 14 of 88 randomly selected students admitted having cheated at least once. Is this strong evidence that the teacher was wrong?
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