Confidence Intervals (1 sample)
Name _______________________________
Chapter 9 Homework
Read each problem carefully. Write your answer in the blank, or circle the correct answer.
1. In a trial of 200 patients who received 10-mg doses of a drug daily, 28 reported headache as a side effect.
What is the point estimate for the population proportion of patients who reported a headache as a side effect?
a) 200
b) 28
c) 0.28
d) 0.14
Construct a 95% confidence interval for the population proportion of patients who receive the drug and report
headache as a side effect. (do not round)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true_________________ of _____ patients who report headache as a side
effect is between _______________ and _______________.
2. Explain what “90% confidence” means in a 90% confidence interval.
a) The probability that the value of the parameter lies between the lower and upper bounds of the
interval is 90%. The probability that it does not is 10%.
b) The value of the parameter lies with 90% of a standard deviation of the estimate.
c) If 100 different confidence intervals are constructed, each based on a different sample of size n
from the same population, then we expect 90 of the intervals to include the parameter and 10 to
not include the parameter.
3. A poll found that 399 of 2,279 adults aged 18 or older have at least one tattoo.
What is the point estimate for the population proportion of adults who have at least one tattoo?
a) 2,279
b) 0.175
c) 399
d) 0.18
Construct a 95% confidence interval for the population proportion of adults who have at least one tattoo.
(do not round)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true_________________ of ________ adults who have at least one tattoo
is between _______________ and _______________.
Construct a 99% confidence interval for the population proportion of adults who have at least one tattoo.
(do not round)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true_________________ of ________ adults who have at least one tattoo
is between _______________ and _______________.
What happens as you increase the confidence level from 95% to 99%?
a) Increasing the level of confidence widens the interval.
b) Increasing the level of confidence has no effect on the interval.
c) Increasing the level of confidence narrows the interval.
d) It is not possible to tell the effect.
4. A researcher wishes to estimate the proportion of adults who have high-speed internet access.
What sample size should be obtained if she wishes the estimate to be within 0.03 with 95% confidence?
What sample size should be obtained if she wishes the estimate to be within 0.03 with 95% confidence and she
uses a previous estimate of 0.38?
5. A poll was conducted that asked 1,010 people how many books they read in the past year.
Results indicated that x = 10.4 books and s = 16.6 books.
What is the point estimate for the mean number of books people read?
a) 16.6
b) 10.4
c) 1,010
d) 0.0103
Construct a 90% confidence interval for the mean number of books that all people read.
(do not round)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true_____________ number of books that ______ adults have read
is between _______________ and _______________ books.
6. In a random sample of 33 criminals convicted of a certain crime, it was determined that the mean length
of sentencing was 65 months, with a standard deviation of 10 months.
What is the point estimate for the mean length of sentencing for crimes of this type?
a) 10
b) 33
c) 65
d) 1.97
Construct a 95% confidence interval for the mean length of sentencing for all crimes of this type.
(do not round)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true_____________ length of sentencing for ______ crimes of this type
is between _______________ and _______________ months.
7. The following data represent the asking price of a simple random samples of homes for sale.
$ 177,500
$ 143,000
$ 459,900
$ 179,500
$ 279,900
$ 205,800
$ 290,000
$ 147,800
$ 219,900
$ 239,900
$ 187,500
$ 264,900
Construct a 99% confidence interval for the mean asking price of a home.
(do not round)
(__________ ,
__________)
Construct a 99% confidence interval for the mean asking price of a home with the outlier removed.
Note: The “outlier” is the one home price that is larger than all the others.
(do not round)
(__________ ,
__________)
What effect does removing the outlier have on the confidence interval?
a) Removing the outlier caused the width of the confidence interval to increase.
b) Removing the outlier caused the width of the confidence interval to decrease.
c) Removing the outlier had no effect on the width of the confidence interval.
8. A real estate agent wants to estimate the average age of people buying investment property in his area.
He randomly selects 15 of his clients who purchased an investment property and obtains the data shown.
The buyer ages are approximately normally distributed and the sample does not contain any outliers.
32
38
35
57
37
57
58
38
51
63
30
55
64
64
28
Construct a 90% confidence interval for the mean age for all the real estate agent’s clients who purchased
investment property. (do not round)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true_____________ age for ______ the real estate agent’s clients who
purchased investment property is between _______________ and _______________ years.
9. Find the critical values
 2L and  2R
 2L
= _______________
 2R
= _______________
for a 90% confidence level and a sample size of 30.
10. Data was gathered representing the number of days of the growing season over the last 10 years in a
certain geographic area. It is known that the data are normally distributed and that s = 23.73 days.
What is the point estimate for the standard deviation of the number of days in the growing season?
a) 10
b) 2.37
c) 237
d) 23.73
Construct a 99% confidence interval for the population standard deviation of the number of days in the
growing season. (round to 2 decimals)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true_____________________ of the number of days in the growing season
is between _______________ and _______________ days.
11. Data was gathered representing the age (in weeks) at which babies first crawl based on a survey of 12
mothers. It is known that the data are normally distributed and that s = 13.50 weeks.
What is the point estimate for the standard deviation of the age at which babies first crawl?
a) 13.5
b) 12
c) 162
d) 1.125
Construct a 90% confidence interval for the population standard deviation of the age (in weeks) at which
babies first crawl. (round to 2 decimals)
(__________ ,
__________)
Interpret the interval.
I am _______% confident that the true____________________ of the age at which ______ babies first crawl
is between _______________ and _______________ weeks.