DIRECTIONS: SHOW ALL WORK TO EARN CREDIT. EACH QUESTION IS WORTH 10 POINTS
1. In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12
months, the mean weight loss was found to be 2.1 lb., with a standard deviation of 4.8 lb.
Construct a 90% confidence interval estimate of the mean weight loss of all such subjects. Does
the Atkins program appear to be effective? Does it appear to be practical? Explain.
2. Listed below are the ages (in years) of randomly selected race car drivers. Construct a 95%
confidence interval estimate of the mean age of all race car drivers.
32 32 33 33 41 29 38 32 33 23 27 45 52 29 25
a) Find a 99% confidence interval for μ if n = 100
b) Find a 99% confidence interval for μ if n = 400
c) Find the widths of the confidence intervals you calculated in parts a and b. What is the effect on
the width of a confidence interval of quadrupling the sample size while holding the confidence
level constant?
4. A sample of 106 body temperatures has a mean of 98.20oF and a standard deviation of 0.62oF.
Construct a 95% confidence interval estimate of the mean body temperature of the entire
population. What does the result suggest about the common belief that 98.6oF is the mean body
temperature?
5. Listed below are the numbers of years it took for a random number of college students to earn
bachelor’s degree (based on a research study). Construct a 99% confidence interval estimate of
the mean time required for all college students to earn bachelor’s degrees. Does the confidence
Interval contain a value of 4 years? What conclusion can you draw from your answer?
4 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 4.5 6 6 8 9 9 13 13 15
6. In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at
least one prescription medication.
a) How many of the 3005 subjects used at least one prescription medication?
b) Construct a 90% confidence interval estimate of percentage of adults aged 57 through 85 years
who used at least one prescription medication
c) What do the results tell us about college students who used at least one prescription
medication?
a) Among the 514 human resource professionals, how many of them said that the appearance of a
job applicant is most important for a good first impression?
b) Construct a 99% confidence interval estimate of the proportion of all human resource
professionals believing that the appearance of a job applicant is most important for a good first
impression.
c) Repeat part b using a confidence level of 80%
d) Compare the confidence intervals from parts (b) and (c) and identify the interval that is wider.
Why do you think it is wider?
8. USA Today reported on the results of an opinion poll in which adults were asked what one thing
they are most likely to do when they are home sick with a cold or flu. In the survey, 63% said
that they are most likely to sleep and 18% said that they would watch television. Although the
sample size was not reported, typically opinion polls typically opinion polls include
approximately 1,000 randomly selected respondents.
a) Assuming a sample of 1,000 for this poll, construct a 95% confidence interval for the true
percentage of all adults who would choose to sleep when they are at home sick.
b) If the true percentage of adults who would choose to sleep when they are at home sick is 70%,
would you be surprised? Explain.
SAMPLING DISTRIBUTION OF SAMPLE MEANS
9.
NAME: DATE:
ESTIMATING POPULATION MEAN
DIRECTIONS: SHOW ALL WORK TO EARN CREDIT. EACH QUESTION IS WORTH 10 POINTS
1. In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12
months, the mean weight loss was found to be 2.1 lb., with a standard deviation of 4.8 lb.
Construct a 90% confidence interval estimate of the mean weight loss of all such subjects. Does
the Atkins program appear to be effective? Does it appear to be practical? Explain.
2. Listed below are the ages (in years) of randomly selected race car drivers. Construct a 95%
confidence interval estimate of the mean age of all race car drivers.
32 32 33 33 41 29 38 32 33 23 27 45 52 29 25
3. The mean and standard deviation of a random sample of n measurements are respectively equal
to 33.9 and 3.3.
a) Find a 99% confidence interval for μ if n = 100
b) Find a 99% confidence interval for μ if n = 400
c) Find the widths of the confidence intervals you calculated in parts a and b. What is the effect on
the width of a confidence interval of quadrupling the sample size while holding the confidence
level constant?
4. A sample of 106 body temperatures has a mean of 98.20oF and a standard deviation of 0.62oF.
Construct a 95% confidence interval estimate of the mean body temperature of the entire
population. What does the result suggest about the common belief that 98.6oF is the mean body
temperature?
5. Listed below are the numbers of years it took for a random number of college students to earn
bachelor’s degree (based on a research study). Construct a 99% confidence interval estimate of
the mean time required for all college students to earn bachelor’s degrees. Does the confidence
Interval contain a value of 4 years? What conclusion can you draw from your answer?
4 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 4.5 6 6 8 9 9 13 13 15
ESTIMATING POPULATION PROPORTION
6. In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at
least one prescription medication.
a) How many of the 3005 subjects used at least one prescription medication?
b) Construct a 90% confidence interval estimate of percentage of adults aged 57 through 85 years
who used at least one prescription medication
c) What do the results tell us about college students who used at least one prescription
medication?
7. In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job
applicant is most important for a good first impression.
a) Among the 514 human resource professionals, how many of them said that the appearance of a
job applicant is most important for a good first impression?
b) Construct a 99% confidence interval estimate of the proportion of all human resource
professionals believing that the appearance of a job applicant is most important for a good first
impression.
c) Repeat part b using a confidence level of 80%
d) Compare the confidence intervals from parts (b) and (c) and identify the interval that is wider.
Why do you think it is wider?
8. USA Today reported on the results of an opinion poll in which adults were asked what one thing
they are most likely to do when they are home sick with a cold or flu. In the survey, 63% said
that they are most likely to sleep and 18% said that they would watch television. Although the
sample size was not reported, typically opinion polls typically opinion polls include
approximately 1,000 randomly selected respondents.
a) Assuming a sample of 1,000 for this poll, construct a 95% confidence interval for the true
percentage of all adults who would choose to sleep when they are at home sick.
b) If the true percentage of adults who would choose to sleep when they are at home sick is 70%,
would you be surprised? Explain.
SAMPLING DISTRIBUTION OF SAMPLE MEANS
9. Suppose a random variable x has a mean of 20 and a standard deviation of 5. Determine the
mean and the standard deviation of the sample mean for each of the following sample sizes
(Assume the population is infinite).
a) n = 35 (3 pts)
b) n = 50 (3 pts)
c) n = 75 (3pts)
d) What can you conclude about the standard deviation of the sample mean as n increases?
SAMPLING DISTRIBUTION OF SAMPLE PROPORTIONS
10. In a city poll, 70% of the people prefer Candidate A. Suppose 30 people from this city
were sampled.
(a) What is the mean of the sampling distribution of ? (1 pt)
(b) What is the standard error of ? (2 pts)
(c) What is the probability that 80% or more of this sample will prefer Candidate A? (3
pts)
(d) What is the probability that 45% or more of this sample will prefer some other
candidate? (4 pts(Assume the population is infinite).
a) n = 35 (3 pts)
b) n = 50 (3 pts)
c) n = 75 (3pts)
d) What can you conclude about the standard deviation of the sample mean as n increases?
SAMPLING DISTRIBUTION OF SAMPLE PROPORTIONS
10. In a city poll, 70% of the people prefer Candidate A. Suppose 30 people from this city
were sampled.
(a) What is the mean of the sampling distribution of ? (1 pt)
(b) What is the standard error of ? (2 pts)
(c) What is the probability that 80% or more of this sample will prefer Candidate A? (3
pts)
(d) What is the probability that 45% or more of this sample will prefer some other
candidate? (4 pts
