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The fraction or ratio of a sample possessing a certain trait is called a:
Population.
Mean.
Confidence interval.
Proportion.
Proportion is the same as fraction is the same as ratio is the same as percentage.
References
Multiple Choice
Learning Objective: 08-03 Compute
and interpret a confidence interval
for a population mean when the
population standard deviation is
unknown.
An economist wants to estimate the proportion of Canadians who own their homes. A random sample of 800 people reveals 544 own their homes. Develop a 95%
confidence interval for the population proportion.
0.68 ± 0.053
0.68 ± 0.032
0.32 ± 0.032
0.68 ± 0.027
We have:
x = 544 people,
n
= 800 people, 95% confidence interval
For a 95% confidence interval z = 1.96.
First calculate the sample proportion: So, we estimate 68% of people own their homes. The 95% confidence interval is
.
References
Multiple Choice
Learning Objective: 08-03 Compute
and interpret a confidence interval
for a population mean when the
population standard deviation is
unknown.
✓
✓
3.
Award: 10 out of 10.00 points
4.
Award: 10 out of 10.00 points
5.
Award: 10 out of 10.00 points
When do we apply the finite population correction factor?
When our sample size is 5% or more of our finite population size.
When we know exactly what the population size is.
Anytime we take a sample.
Anytime we are calculating a sample size.
References
Multiple Choice
Learning Objective: 08-06 Adjust a
confidence interval for a finite
population.
We know the total population is 3,000. 30% of the 500 people sampled say that they prefer hot dogs to hamburgers. Prepare a 95% confidence interval for the proportion
that prefer hot dogs.
26.00% to 34.00% prefer hot dogs.
26.33% to 33.67% prefer hot dogs.
16.67%
Cannot be determined from the information provided.
References
Multiple Choice
Learning Objective: 08-04 Compute
and interpret a confidence interval
for a population proportion.
Learning Objective: 08-05 Calculate the required sample size to estimate
a population mean or population proportion.
The necessary sample size depends on:
The level of confidence desired
The allowable margin of error
The variability in the population of study
The level of confidence desired, the allowable margin of error, and the variability in the population of study.
The necessary sample size depends on all three of the factors listed.
References
Multiple Choice
Learning Objective: 08-06 Adjust a
confidence interval for a finite
population.
✓
✓
✓
6.
Award: 10 out of 10.00 points
7.
Award: 10 out of 10.00 points
A pilot study shows that 64% of people living in the downtown core are single. A market research company wants to verify this claim. The company requires a 95%
confidence interval. How many residents should be interviewed to keep the margin of error within 0.02 of the population proportion?
23
9604
2213
6147
We have:
p
= 0.64, E
= 0.02, 95% confidence interval
For a 95% confidence interval z = 1.96.
A random sample of 2213 people is required.
References
Multiple Choice
Learning Objective: 08-06 Adjust a
confidence interval for a finite
population.
A random sample of 300 drivers revealed that 96 of them had received a speeding ticket in the last 3 months. Construct a 95% confidence interval for the number of drivers
who receive speeding tickets over a three-month period.
0.32 ± 0.027
0.32 ± 0.001
0.32 ± 0.069
0.32 ± 0.053
We have:
x
= 96 drivers, n
= 300 drivers, 95% confidence interval
For a 95% confidence interval z = 1.96.
First calculate the sample proportion: So, we estimate 32% of drivers have received a speeding ticket in the past 3 months. The 95% confidence interval is
.
References
Multiple Choice
Learning Objective: 08-04 Compute
and interpret a confidence interval
for a population proportion.
✓
✓
8.
Award: 10 out of 10.00 points
9.
Award: 10 out of 10.00 points
10.
Award: 10 out of 10.00 points
American Express cardholders are reported to spend more per purchase than either VISA or MasterCard cardholders. The average purchase at a giftware store is $70. The
owner conducts a random survey of 120 people who use their American Express card and finds 84 of them make purchases in excess of the average $70. Conduct a 90%
confidence interval for the number of American Express cardholders that make purchases greater than $70.
0.70 ± 0.002
0.70 ± 0.003
0.70 ± 0.069
0.70 ± 0.042
We have:
x
= 84 cardholders, n
= 120 cardholders, 90% confidence interval
For a 90% confidence interval z = 1.645.
First calculate the sample proportion: So, we estimate 70% of American Express cardholders spend in excess of the average purchase. The 90% confidence interval is
.
References
Multiple Choice
Learning Objective: 08-04 Compute
and interpret a confidence interval
for a population proportion.
A finite population is:
a large population.
an exactly known population size.
5% of the total population.
a population from which samples were taken.
References
Multiple Choice
Learning Objective: 08-05 Calculate
the required sample size to estimate
a population mean or population
proportion.
Determining a sample size depends on all of these except:
confidence level.
population size.
maximum allowable error.
variation in the population.
Determining sample size does not depend on the population size. Population size has no bearing on how large or small a sample size will be. If there is no prior estimate of
the population proportion, we use p
= 0.5 to maximize the sample size.
References
Multiple Choice
Learning Objective: 08-06 Adjust a
confidence interval for a finite
population.
✓
✓
✓
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