the alarm. The scanner has a 98% chance of detecting an active chip (meaning the material has not
been checked out) and setting off the alarm. The scanner also has a 3% chance of sounding the
alarm when someone passes through without an active chip. It is estimated that 0.5% of library
customers actually try to leave the library with an active chip. What is the probability that, if the
alarm sounds, the patron leaving the library has an item with an active chip?
A. 0.0049
B. 0.0348
C. 0.1410
D. 0.9700
E. 0.9800
Which of the following is the best description of the power of a significance test?
A. The probability that the null hypothesis is true.
B. The probability of getting a Type I error.
C. The probability of getting a Type II error.
D. The probability of getting a test statistic at least as extreme as the actual test statistic, if the null
hypothesis is true.
E. The probability of rejecting the null hypothesis if it is, in fact, false.
A school board of a large school district is proposing a new dress code for students. Some students
feel that this dress code unfairly targets female students. To see if there is a difference between
boys and girls in their opposition to the new dress code, they conduct a poll of 60 randomly
selected male and 70 randomly selected female high school students in the district. They find that 66
females oppose the dress code and 50 males oppose the dress code. Which of the following
explains why a two-proportion z -test is not appropriate?
A. The sample sizes are different.
B. The sample sizes are too large.
C. The number of successes and the number of failures for the two groups are not all large enough.
D. The shapes of the population distributions are not known.
E. The population standard deviations are not known.
- Researchers are conducting an experiment using a significance level of 0.05. The null hypothesis
is, in fact, false. If they modify their experiment to use twice as many experimental units for each
treatment, which of the following would be true?
A. The probability of a Type I error and the probability of a Type II error would both decrease.
B. The probability of a Type I error and the power would both increase.
C. The probability of a Type II error and the power would both increase.
D. The probability of a Type I error would stay the same and the power would increase.
E. The probability of a Type II error would stay the same and the power would increase. - A producer of skin care products has created a new formula for its cream to cure acne. To compare
the effectiveness of the new cream to that of the old cream, it conducted a double-blind randomized
experiment. Volunteers with acne tried the old formula on one side of their face and the new formula
on the other, and which side got which formula was determined randomly. The response variable
was the difference in the number of pimples (old formula – new formula). Which is the correct
significance test to perform?