Download 7.3 - Confidence Intervals Review

NAME ___________________________________
Confidence Interval Practice #2
DATE _____________
PERIOD _____
1. The critical value, z*, used for constructing a 96% confidence interval for a population mean  is
a. 1.645.
b. 2.054.
c. 2.326.
d. 2.576.
For questions 2 and 3: A researcher used a new drug to treat 100 subjects with high cholesterol. For the patients in
the study, after two months of treatment the average decrease in cholesterol level was 80 milligrams per deciliter
(mg/dl). Assume that the decrease in cholesterol after two months of taking the drug follows a Normal distribution, with
unknown mean  and standard deviation  = 20 mg/dl. The researcher will construct a 90% confidence interval to
estimate .
2. The researcher’s 90% confidence interval for  is
a. 78 mg/dl to 82 mg/dl.
b. 76.71 mg/dl to 83.29 mg/dl.
c. 60 mg/dl to 100 mg/dl.
d. 47.1 mg/dl to 112.9 mg/dl.
3. The margin of error associated with a 90% confidence interval for the researcher’s 90% confidence interval for  is
a. 1.645 mg/dl.
b. 20 mg/dl.
c. 2 mg/dl.
d. 3.29 mg/dl.
4. You measure the lifetime (in miles of driving use) of a random sample of 25 tires of a certain brand. The sample
mean is 64,200 miles. Suppose that the lifetimes for tires of this brand follow a normal distribution, with unknown
mean  and standard deviation  = 4,800 miles. A 95% confidence interval for  is about
a. 62,318.4 miles to 66,081.6 miles.
b. 62,620.8 miles to 65,779.2 miles.
c. 63,240 miles to 65,160 miles.
d. 54,792 miles to 73,608 miles.
5. You want to estimate the mean SAT score for a population of students with a 90% confidence interval.
Assume that the population standard deviation is  = 100. If 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
.
6. You have measured the systolic blood pressure of a random sample of 25 employees of a
company located near you. A 95% confidence interval for the mean systolic blood pressure for the
employees of this company is (122, 138). Which of the following statements gives a valid interpretation
of this interval?
(a) Ninety-five percent of the sample of employees has a systolic blood pressure between 122 and 138.
(b) Ninety-five percent of the population of employees has a systolic blood pressure between 122 and 138.
(c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain
the population mean systolic blood pressure.
(d) The probability that the population mean blood pressure is between 122 and 138 is .95.
(e) If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.
7. A 99% confidence interval is found to be (42,136).
a) What is the sample mean?
b) What is the margin of error?
8. What is the z* value if you wanted to calculate a 94.5% confidence interval?
9. You measure the weights of a random sample of 24 male runners. The sample mean is x = 60 kilograms (kg).
Suppose that the standard deviation of the population is known to be  = 5kg.
a) What is  x , the standard deviation of x ?
b) Give a 95% confidence interval for  , the mean of the population from which the sample is drawn.
c) Are you quite sure that the average weight of the population of runners is less than 65 kg?
Explain why or why not.
d) Find a 99% confidence interval for the mean weight  of the population of male runners.
e) Is the 99% confidence interval wider or narrower than the 95% interval?
Explain why this is true.
10. Crop researchers plant 50 plots with a new variety of corn. The average yield for these plots is x = 130 bushels per
acre. Assume that  = 10 bushels per acre.
a) Find the 90% confidence interval for the mean yield  for this variety of corn.
b) Find the 95% confidence interval.
c) How do the margins of error in (a) and (b) change as the confidence level increases?
11. Suppose that the crop researchers in #10 obtained the same value of x from a sample of 100 plots rather than 50.
a) Compute the 95% confidence interval for the mean yield  .
b) Is the margin of error larger or smaller than the margin of error found for the sample of 50 plots in #10?
Explain why this occurs.