AP Statistics
Mrs. LaPlaca
Chapter 10
Section 10.1: Confidence Intervals
Practice Multiple Choice Problems.
1. You want to compute a 96% confidence interval for a population mean. Assume that
the population standard deviation is known to be 10 and the sample size is 50. The
value of z* to be used in this calculation is
(a) 1.960
(b) 1.645
(c) 1.7507
(d) 2.0537
(e) None of the above. The answer is
.
2. You want to estimate the mean SAT score for a population of students with a 90%
you want the margin of error to be approximately 10, you will need a sample size of
(a) 16
(b) 271
(c) 38
(d) 1476
(e) None of the above. The answer is
.
3. Which among the following would result in the narrowest confidence interval?
(a) Small sample size and 95% confidence
(b) Small sample size and 99% confidence
(c) Large sample size and 95% confidence
(d) Large sample size and 99% confidence
4. Which of the following are true statements?
I. Even if the original population is badly skewed, the mean of the set of all sample
means from all samples of a given size will equal the mean of the population.
II. If the original population is very large it is usually advisable to work with a large
sample.
III. A confidence interval estimate for a population mean is used to eliminate the
element of chance from the estimation.
(a)
(b)
(c)
(d)
(e)
I only
II only
III only
I and III
I, II, and III
5. Hospital administrators wish to determine the average length of stay for all surgical
patients. A statistician determines that for a 95% confidence interval estimate of the
average length of stay to within ±.50 days, 100 surgical patients’ records would have to
be examined. How many records should be looked at for a 95% confidence level
estimate to within ±.25 days.
(a) 25
(b) 50
(c) 200
(d) 400
(e) There is not enough information given to determine the necessary sample size.
6. Suppose (25, 30) is a 90% confidence interval estimate for a population mean m .
Which of the following are true statements?
I. There is a .90 probability that m is between 25 and 30.
II. If 100 random samples of the given size are picked and a 90% confidence
interval estimate is calculated from each, then m will be in 90 of the resulting
intervals.
III. If 90% confidence intervals are calculated from all possible samples of the
given size, m will be in 90% of these intervals.
(a)
(b)
(c)
(d)
(e)
I only
II only
III only
I and III
I, II, and III
7. 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 absolutely that you will get a larger interval. One can only
say the chance of obtaining a larger interval is 0.05
8. A 95% confidence interval for the mean m of a population is computed from a random
sample and found to be 9 ± 3. We may conclude that
(a) There is a 95% probability that m 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 m , approximately 95% of these intervals would
contain m .
(d) If we took many, many additional random samples and from each computed a
95% confidence interval for m , 95% of them would cover the values from 6 to
12.
(e) All of the above.
9. Suppose we want a 90% confidence interval for the average amount spent on books by
freshmen in their first year at a major university. The interval is to have a margin of error
of $2, and the amount spent has a normal distribution with a standard deviation s = $30.
The number of observations required is closest to
(a)
(b)
(c)
(d)
(e)
25.
30.
608.
609.
865.
10. The value of z* required for a 70% confidence interval is
(a) -0.5244
(b) 0.6179
(c) 1.036
(d) 0.5244
(e) The answer can’t be determined from the information given.
(f) None of the above. The answer is _____________________.