Assignment: 3-2 MyStatLab: Module Three Problem Set | Complete Solution

Course: MAT-240

Assignment: 3-2 MyStatLab: Module
Three Problem Set

Compute the critical value z that corresponds to a % level of confidence. α / 2 91
zα / 2 =
(Round to two decimal places as needed.)
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the
number of individuals in the sample with the specified characteristic, x, for the sample size provided.
Lower bound = 0.293, upper bound = 0.507, n = 1500
The point estimate of the population proportion is .
(Round to the nearest thousandth as needed.)
The margin of error is .
(Round to the nearest thousandth as needed.)
The number of individuals in the sample with the specified characteristic is .
(Round to the nearest integer as needed.)
Construct a confidence interval of the population proportion at the given level of confidence.
x = 120, n = 1100, 95% confidence
The upper bound of the confidence interval is .
(Round to the nearest thousandth as needed.)
The lower bound of the confidence interval is .
(Round to the nearest thousandth as needed.)
A poll of adults in a certain country found that % identified themselves as the followers of some religion. The
margin of error was percentage points with % confidence.
1125 23
5 95
Which of the following represents a reasonable interpretation of the survey results?
A. In % of samples of adults in a certain country, the proportion who identify themselves as the
followers of some religion is between % and %.
95
18 28
B. There is % confidence that the proportion of adults in a certain country who identify themselves as
the followers of some religion is between % and %.
95
18 28
C. There is between % and % confidence that % of adults in a certain country identify
themselves as the followers of some religion.
90 100 23
D. There is % confidence that % of adults in a certain country identify themselves as the followers of
some religion.
95 23
5.
6.
7.
In a trial of patients who received 10-mg doses of a drug daily, reported headache as a side effect. Use this
information to complete parts (a) through (d) below.
125 35
(a) Obtain a point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported
headache as a side effect.
p = (Round to two decimal places as needed.)
(b) Verify that the requirements for constructing a confidence interval about p are satisfied.
Are the requirements for constructing a confidence satisfied?
A. Yes, the requirements for constructing a confidence interval are satisfied.
B. No, the requirement that each trial be independent is not satisfied.
C. No, the requirement that np 1 − p is greater than 10 is not satisfied.
D. No, the requirement that the sample size is no more than 5% of the population is not satisfied.
(c) Construct a % confidence interval for the population proportion of patients who receive the drug and report headache
as a side effect.
99
The 99% confidence interval is ( , ).
(Round to three decimal places as needed.)
(d) Interpret the confidence interval. Which statement below best interprets the interval?
A. We are 99% confident that the interval contains the true value of p.
B. There is a 99% chance that the true value of p will fall in the interval.
C. There is a 99% chance that the true value of p will not fall in the interval.
D. We are 99% confident that the interval does not contain the true value of p.
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be
obtained if she wishes the estimate to be within 0.01 with 95% confidence if
(a) she uses a previous estimate of 0.36?
(b) she does not use any prior estimates?
(a) n = (Round up to the nearest integer.)
(b) n = (Round up to the nearest integer.)
Katrina wants to estimate the proportion of adults who read at least 10 books last year. To do so, she obtains a simple
random sample of 100 adults and constructs a 95% confidence interval. Matthew also wants to estimate the proportion of
adults who read at least 10 books last year. He obtains a simple random sample of 400 adults and constructs a 99%
confidence interval. Assuming both Katrina and Matthew obtained the same point estimate, whose estimate will have the
smaller margin of error? Justify your answer.
Whose estimate will have the smaller margin of error and why?
A. Matthew's estimate will have the smaller margin of error because the larger sample size more than
compensates for the higher level of confidence.
B. Matthew's estimate will have the smaller margin of error because the sample size is larger and the level
of confidence is higher.
C. Katrina's estimate will have the smaller margin of error because the sample size is smaller and the level
of confidence is lower.
D. Katrina's estimate will have the smaller margin of error because the lower level of confidence more than
compensates for the smaller sample size.
8.
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1: Table of t-Distribution Areas
Determine the t-value in each of the cases.
Click the icon to view the table of areas under the t-distribution. 1
(a) Find the t-value such that the area in the right tail is 0.05 with 22 degrees of freedom.
(Round to three decimal places as needed.)
(b) Find the t-value such that the area in the right tail is 0.005 with 30 degrees of freedom.
(Round to three decimal places as needed.)
(c) Find the t-value such that the area left of the t-value is 0.025 with 23 degrees of freedom. [Hint: Use symmetry.]
(Round to three decimal places as needed.)
(d) Find the critical t-value that corresponds to 60% confidence. Assume 11 degrees of freedom.
(Round to three decimal places as needed.)
9.
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Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 19, upper bound is 31.
The point estimate of the population mean is .
The margin of error for the confidence interval is .
10. In a survey, adults in a certain country were asked how many hours they worked in the previous week. Based on
the results, a 95% confidence interval for mean number of hours worked was lower bound: and upper bound:
. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable,
explain the flaw.
1400
39.2
45.6
(a) There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between
39.2 hours and 45.6 hours.
A. Flawed. This interpretation implies that the mean is only for last week.
B. Correct
C. Flawed. This interpretation makes an implication about individuals rather than the mean.
D. Flawed. This interpretation implies that the population mean varies rather than the interval.
(b) We are 95% confident that the mean number of hours worked by adults in this country in the previous week was
between 39.2 hours and 45.6 hours.
A. Correct
B. Flawed. This interpretation makes an implication about individuals rather than the mean.
C. Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within
the interval.
D. Flawed. This interpretation implies that the population mean varies rather than the interval.
(c) 95% of adults in this country worked between 39.2 hours and 45.6 hours last week.
A. Flawed. This interpretation makes an implication about individuals rather than the mean.
B. Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within
the interval.
C. Flawed. This interpretation implies that the mean is only for last week.
D. Correct
(d) We are 95% confident that the mean number of hours worked by adults in a particular area of this country in the
previous week was between 39.2 hours and 45.6 hours.
A. Flawed. This interpretation makes an implication about individuals rather than the mean.
B. Flawed; the interpretation should be about the mean number of hours worked by adults in the
whole country, not about adults in the particular area.
C. Correct
D. Flawed. This interpretation implies that the population mean varies rather than the interval.
11. A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random
sample of people age 15 or older, the mean amount of time spent eating or drinking per day is hours with a
standard deviation of hour. Complete parts (a) through (d) below.
960 1.27
0.65
(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample
size is needed to construct a confidence interval for the mean time spent eating and drinking each day.
A. The distribution of the sample mean will always be approximately normal.
B. Since the distribution of time spent eating and drinking each day is normally distributed, the sample
must be large so that the distribution of the sample mean will be approximately normal.
C. The distribution of the sample mean will never be approximately normal.
D. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed
right), the sample must be large so that the distribution of the sample mean will be approximately
normal.
(b) In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along with the fact that the
data were obtained using a random sample, satisfies the requirements for constructing a confidence interval.
A. The sample size is less than 10% of the population.
B. The sample size is greater than 10% of the population.
C. The sample size is less than 5% of the population.
D. The sample size is greater than 5% of the population.
(c) Determine and interpret a % confidence interval for the mean amount of time Americans age 15 or older spend
eating and drinking each day.
90
Select the correct choice below and fill in the answer boxes, if applicable, in your choice.
(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)
A. There is a % probability that the mean amount of time spent eating or drinking per day is between
and hours.
90
B. The nutritionist is % confident that the amount of time spent eating or drinking per day for any
individual is between and hours.
90
C. The nutritionist is % confident that the mean amount of time spent eating or drinking per day is
between and hours.
90
D. The requirements for constructing a confidence interval are not satisfied.
(d) Could the interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking each day?
Explain.
A. Yes; the interval is about the mean amount of time spent eating or drinking per day for people people
age 15 or older and can be used to find the mean amount of time spent eating or drinking per day
for 9-year-olds.
B. No; the interval is about people age 15 or older. The mean amount of time spent eating or drinking per
day for 9-year-olds may differ.
C. No; the interval is about individual time spent eating or drinking per day and cannot be used to find the
mean time spent eating or drinking per day for specific age.
D. Yes; the interval is about individual time spent eating or drinking per day and can be used to find the
mean amount of time a 9-year-old spends eating and drinking each day.
E. A confidence interval could not be constructed in part (c).
12. Based on interviews with SARS patients, researchers found that the mean incubation period was days, with a
standard deviation of days. Based on this information, construct a 95% confidence interval for the mean incubation
period of the SARS virus. Interpret the interval.
96 5.6
14.2
The lower bound is days. (Round to two decimal places as needed.)
The upper bound is days. (Round to two decimal places as needed.)
Interpret the interval. Choose the correct answer below.
A. There is 95% confidence that the mean incubation period is less than the lower bound of the interval.
B. There is 95% confidence that the mean incubation period is greater than the upper bound of the
interval.
C. There is a 95% probability that the mean incubation period lies between the lower and upper bounds of
the interval.
D. There is 95% confidence that the mean incubation period lies between the lower and upper bounds of
the interval.
13.
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2: Table of t-Distribution Areas
The following data represent the asking price of a simple random sample
of homes for sale. Construct a % confidence interval with and without
the outlier included. Comment on the effect the outlier has on the
confidence interval.
99
$249,500 $279,900 $219,900
$143,000 $205,800 $267,000
$459,900 $247,900 $187,500
$159,900 $147,800 $264,900
Click the icon to view the table of areas under the t-distribution. 2
(a) Construct a 99% confidence interval with the outlier included.
($ , $ )
(Round to the nearest integer as needed.)
(b) Construct a 99% confidence interval with the outlier removed.
($ , $ )
(Round to the nearest integer as needed.)
(c) Comment on the effect the outlier has on the confidence interval.
The outlier caused the width of the confidence interval to increase.
The outlier caused the width of the confidence interval to decrease.
The outlier had no effect on the width of the confidence interval.
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A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to
estimate the mean HDL cholesterol within points with confidence assuming based on earlier studies?
Suppose the doctor would be content with confidence. How does the decrease in confidence affect the sample
size required?
2 99% s = 19.3
95%
A 99% confidence level requires subjects. (Round up to the nearest subject.)
A 95% confidence level requires subjects. (Round up to the nearest subject.)
How does the decrease in confidence affect the sample size required?
A. Decreasing the confidence level increases the sample size needed.
B. The sample size is the same for all levels of confidence.
C. Decreasing the confidence level decreases the sample size needed.