SCI 1020 – QUIZ Confidence Intervals with Complete Solutions
1. A 99% confidence interval for the average weight μ of a population is computed from
a random sample and found to be ±6 2, or 4 to 8. We may conclude that there is a
99% probability that μ is between 4 and 8.
2. A researcher selects a random sample. A 90% confidence interval for a population
mean μ has the property that if we repeatedly selected our random sample in exactly
the same way, each time constructing a different 90% confidence interval for μ, then
in the long run 90% of those intervals would contain μ.
3. Crop researchers plant 100 plots with a new variety of corn. The average yield for
these plots is = 130 bushels per acre. Assume that the yield per acre for the new
variety of corn follows a normal distribution with unknown mean µ and standard
deviation σ = 20 bushels per acre. A 90% confidence interval for µ is: 130 ± 3.29.
4. The amount of time customers at a “Quick-Change” motor oil store spend waiting for
their cars to be serviced has the Normal distribution with mean μ and standard
deviation σ = 4 minutes. It is company policy that the customer wait time should be
20 minutes (or less). The manager of a particular store selects a random sample of 150
customer wait times and observes a mean wait time of 21 minutes.
A 95% confidence interval for the mean waiting time for customers is about 21 ± 0.64
minutes.
5. A researcher is interested in the average time served in jail for robbery. He takes a
sample of 400 convictions, and finds the average time served is = 7.5 years, with
standard deviation s = 3 years. Since the sample is so large, it is reasonable to believe
that s is close to σ. A 95% confidence interval for the average time served in jail for
robbery is: (7.21, 7.79).
6. The scores of a certain population on the Wechsler Intelligence Scale for Children
(WISC) are thought to be Normally distributed with mean μ and standard deviation σ
= 10. A simple random sample of 30 children from this population is taken and each
is given the WISC. The mean of the 30 scores is sample mean = 104.32.
Suppose a histogram of the 30 WISC scores is the following.
Based on this histogram, we would conclude that any confidence interval constructed
from this sample may be used with some reservation due to the sample size just being
large enough for the Central Limit Theorem to apply
7. The critical value, z *, used for constructing a 96% confidence interval for a
population mean μ is 2.054.
8. The amount of time customers at a “Quick-Change” motor oil store spend waiting for
their cars to be serviced has the Normal distribution with mean μ and standard
deviation σ = 4 minutes. It is company policy that the customer wait time should be
1. A 99% confidence interval for the average weight μ of a population is computed from
a random sample and found to be ±6 2, or 4 to 8. We may conclude that there is a
99% probability that μ is between 4 and 8.
2. A researcher selects a random sample. A 90% confidence interval for a population
mean μ has the property that if we repeatedly selected our random sample in exactly
the same way, each time constructing a different 90% confidence interval for μ, then
in the long run 90% of those intervals would contain μ.
3. Crop researchers plant 100 plots with a new variety of corn. The average yield for
these plots is = 130 bushels per acre. Assume that the yield per acre for the new
variety of corn follows a normal distribution with unknown mean µ and standard
deviation σ = 20 bushels per acre. A 90% confidence interval for µ is: 130 ± 3.29.
4. The amount of time customers at a “Quick-Change” motor oil store spend waiting for
their cars to be serviced has the Normal distribution with mean μ and standard
deviation σ = 4 minutes. It is company policy that the customer wait time should be
20 minutes (or less). The manager of a particular store selects a random sample of 150
customer wait times and observes a mean wait time of 21 minutes.
A 95% confidence interval for the mean waiting time for customers is about 21 ± 0.64
minutes.
5. A researcher is interested in the average time served in jail for robbery. He takes a
sample of 400 convictions, and finds the average time served is = 7.5 years, with
standard deviation s = 3 years. Since the sample is so large, it is reasonable to believe
that s is close to σ. A 95% confidence interval for the average time served in jail for
robbery is: (7.21, 7.79).
6. The scores of a certain population on the Wechsler Intelligence Scale for Children
(WISC) are thought to be Normally distributed with mean μ and standard deviation σ
= 10. A simple random sample of 30 children from this population is taken and each
is given the WISC. The mean of the 30 scores is sample mean = 104.32.
Suppose a histogram of the 30 WISC scores is the following.
Based on this histogram, we would conclude that any confidence interval constructed
from this sample may be used with some reservation due to the sample size just being
large enough for the Central Limit Theorem to apply
7. The critical value, z *, used for constructing a 96% confidence interval for a
population mean μ is 2.054.
8. The amount of time customers at a “Quick-Change” motor oil store spend waiting for
their cars to be serviced has the Normal distribution with mean μ and standard
deviation σ = 4 minutes. It is company policy that the customer wait time should be
