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AP Statistics
Chapter 10 Review
Date _________________________
Type I and Type II errors, Power of a Test
1. Recall earlier that we introduced the idea of a test of significance by considering a random sample of 6
cola bottles selected from a manufacturing process that was supposed to fill bottles, on average, to 300 ml.
An appropriate test of significance, with  = 0.05, has hypotheses Ho:  = 300 and Ha:  < 300 when we
suspect that the process is under filling the bottles. The distribution of milliliters of cola is believed to be
normal and is known to have standard deviation  = 3 ml.
a) Find the power of this test against the alternative  = 299 when n = 25.
b) Find the power of this test against the alternative  = 299 when n = 100.
2. The medical director of a large corporation want to know whether or not the mean blood pressure of a
population of executives differs significantly from the national mean of  = 128. He chooses a SRS of 72
executives from this population with  = 15. The hypotheses used would be Ho:  = 128 and Ha:   128.
a) Find the power of this test against the alternative  = 134 given a 5% level of significance.
b) Explain what a Type I error and a Type II error mean in the context of this situation. Which seems
more serious to you?
Check Answers: 1a) 0.5087
1b) 0.9543
2a) 0.9242
Choose the best response for each of the following multiple-choice questions.
1. The value of z*, the upper p critical value, for a 70% confidence interval is
a) -0.5244
b) 1.036
c) 0.5244
d) 0.6179
e) The answer can’t be determined from the information given
1. ___________
2. A 95% confidence interval for the mean u of a population is computed from a random sample with a
sample mean of 9 and margin of error of 3. We may conclude that
a) There is a 95% probability that u is between 6 and 12.
b) There is a 95% probability that the true mean is 9 and a 95% chance the true margin of error is 3.
c) If we took many, many additional random samples and from each computed a 95% confidence interval
for u, approximately 95% of these intervals would contain u.
d) If we took many, many additional random samples and from each computed a 95% confidence interval
for u, 95% of these would cover the values from 6 to 12.
e) All of the above are true.
2. ___________
3. A 95% confidence interval for the mean reading achievement score for a population of third grade
students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same information.
Which of the following statements is correct?
a) The intervals have the same width.
b) The 99% interval is shorter.
c) The 99% interval is longer.
d) The data cannot be used to construct a 99% confidence interval if a 95% confidence interval has
already been constructed.
e) The answer can’t be determined from the given information.
3. ___________
4. Which of the following are correct?
I. The power of a significance test depends on the alternative value of the parameter.
II. The probability of a Type II error is equal to the significance level of the test.
III. Type I and Type II errors only make sense when a significance level has been chosen in
advance.
a) I and II only
b) I and III only
c) II and III only
d) I, II, and III
e) None of the above gives the complete set of true responses.
4. ___________
5. In a test of Ho: u = 100 against Ha: u  100, a sample of size 80 produces z = 0.8 for the value of the
test statistic. The p-value of the test is, therefore, equal to
a) 0.20
b) 0.40
c) 0.29
d) 0.42
e) 0.21
5. ___________
6. To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is
repeatedly weighed a total of n times and the sample mean of the weights is computed. Suppose the scale
readings are normally distributed with unknown mean u and standard deviation  = 0. 01 g. How large
should n be so that a 95% confidence interval for u has a margin of error of 0.0001?
a) 100
b) 196
c) 27,061
d) 10,000
e) 38,416
6. ___________
7. A 95% confidence interval for u is calculated to be (1.7, 3.5). It is now decided to test the hypothesis
Ho: u = 0 against Ha: u  0 at the 5% significance level, using the same data as was used to construct the
confidence interval.
a) We cannot test the hypothesis without the original data.
b) We cannot test the hypothesis at the 5% significance level since the  = 0.05 test is connected to the
97.5% confidence interval.
c) We can only make the connection between hypothesis tests and confidence intervals if the sample sizes
are large.
d) We would reject the null hypothesis at the level  = 0.05.
e) We would accept the null hypothesis at the level  = 0.05.
7. ___________
8. A certain population follows a normal distribution with mean u and standard deviation  = 2.5. You
collect data and test the hypotheses Ho: u = 1 against Ha: u  1. You obtain a p-value of 0.022. Which of
the following is true?
a) A 95% confidence interval for u will include the value 1.
b) A 95% confidence interval for u will include the value 0.
c) A 99% confidence interval for u will include the value 1.
d) A 99% confidence interval for u will include the value of 0.
e) None of these is necessarily true.
8. __________
9. In a statistical test for the equality of a mean, such as Ho: u = 10, if  = 0.05,
a) 95% of the time we will make an incorrect inference.
b) 5% of the time we will say that there is a real difference when there is no difference.
c) 5% of the time we will say that there is no real difference when there is a difference.
d) 95% of the time the null hypothesis will be correct.
e) 5% of the time we will make a correct inference.
9. __________
10. I collect a random sample of size n from a population and from the data collected compute a 95%
confidence interval for the mean of the population. Which of the following would produce a new
confidence interval with larger width (larger margin of error) based on these same data?
a) Use a larger confidence level.
b) Use a smaller confidence level.
c) Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals
will be larger.
d) Increase the sample size.
e) Nothing can guarantee that you will get a larger interval. One can only say that the chance of obtaining
a larger interval is 0.05.
10. __________