Make sure to identify all elements of Test of Hypothesis and Confidence Interval, such as :
Test statistic, Critical value, P-value, Rejection Region, Level of significance,
Error type I and II, Null and Alternate hypotheses, Assumptions.
1. A salesman for a shoe company claimed that runners would record quicker times, on the average, with the
company's brand of sneaker. A track coach decided to test the claim. The coach selected eight runners. Each
runner ran two 100-yard dashes on different days. In one 100-yard dash, the runners wore the sneakers supplied
by the school; in the other, they wore the sneakers supplied by the salesman. Each runner was randomly assigned
the sneakers to wear for the first run. Their times, measured in seconds, were as follows:
For the differences,
= -.225 and
= .276. Assume the population of differences is normal.
2. A new insect spray, type A, is to be compared with a spray, type B, that is currently in use. Two rooms of
equal size are sprayed with the same amount of spray, one room with A, the other with B. Two hundred insects
are released into each room, and after 1 hour the numbers of dead insects are counted." There are 120 dead
insects in the room sprayed with A and 90 in the room sprayed with B. Do the data provide enough evidence to
indicate that spray A is more effective than spray B? Use α = .05.
3. To compare two methods of teaching reading, randomly selected groups of elementary school children were
assigned to each of the two methods for a 6-month period. The criterion for measuring achievement was a
reading comprehension test." The 11 students assigned to method I had a mean score of 64 with a variance of 52.
The 14 students assigned to method II had a mean score of 69 with a variance of 71. Do the data provide enough
evidence to indicate a difference in the mean scores on the comprehension test for the two teaching methods?
Use α = .01.
Magnets are often used by people to treat a variety of disorders.
Researchers recently treated a group of
patients with magnets and another group of patients with a fake magnet treatment.
The results are given below.
Test the claim that the magnet treatment is more effective at lowering pain in arthritis patients:
Mean Pain Reduction
5. A study at the University of Michigan wants to determine student options regarding non-revenue-generating
athletics. Specifically, one question in a survey asks students "Do you think the women's basketball program
should be discontinued?" The data collected revealed that 100 of the 1,000 females surveyed responded "Yes"
and that 400 of the 1,000 males surveyed responded "Yes". Suppose a 99% confidence interval resulted in the
following confidence interval for the true difference in population proportions: (-.5, -.1). Interpret the interval.