Confidence Level Z c
80 1.28
90
95
1.645
1.96 Name: __________________________________________
99 2.575
Confidence Intervals – Quiz Review
1. A news organization reports a confidence interval of (45, 64) for the average number of minutes traveling to work for the population of workers in Washington, DC.
(a) Calculate the point estimate?
(b) What is the margin of error?
2. In a random sample of 45 light bulbs, the mean time of life was 1,505 hours. It is known the population standard deviation is 250 hours.
(a) Construct a 90% confidence interval for the mean life of a light bulb (in hours).
(b) Interpret the confidence level in part (a) in the context of the problem
(c) If you were to construct a 76% confidence interval from the same data, would it be wider or narrower than the interval from (a)?
(d) Construct a 76% confidence interval for the mean life of a light bulb (in hours).

(e) Suppose we want to construct a 99% confidence interval for the mean life of a light bulb (in hours), but we want our margin of error to be no more than 50 hours. What is the smallest sample size we can use?
3. A professor at a large university is curious what the average number of credit hours that students in her class take per term. A random sample of 36 students in her class of 250 students reported the following number of credit hours that they were taking:
12
17
13
17
14
17
14
18
15
18
15
18
15
18
16
19
16
19
16
19
16
20
16
21
21 21 22 22 22 22 23 24 24 24 24 25
The professor knows that the standard deviation of the number of credit hours taken by students
  hours. in her class is
3.5
(a) Construct a 95% confidence interval for the mean number of credit hours taken by students in this professor’s class.
(b) Interpret the interval you found in part (a) in the context of the problem.
(c) If you were to construct an 82% confidence interval from the same data, would it be wider or narrower than the interval from (a)?

(d) Construct an 82% confidence interval for the mean number of credit hours taken by students in this professor’s class.
(e) Suppose we want to construct a 90% confidence interval for the mean number of credit hours taken by students in this professor’s class, but we want our margin of error to be no more than
0.92 hours. What is the smallest sample size we can use?
3. A father is concerned that his teenage son is watching too much television each day, since his son watches an average of 2 hours per day. His son says that his TV habits are not different than those of his friends. Since this father has taken a stats class, he knows that he can actually estimate the average number of hours that teenage boys watch TV each day. The father collects a random sample of television watching times from 30 boys at his son’s high school and gets the following data:
1.9 2.3 2.2 1.9 1.6 2.6 1.4 2.0 2.0 2.2
0.5 2.1 3.0 3.1 1.1 1.2 1.9 2.7 2.2 2.1
0.5 0.8 1.4 1.7 2.4 2.5 2.1 2.2 2.0 2.0
He knows that the standard deviation of the number of hours of TV teenage boys watch per day is  
0.63
hours.
(a) Construct a 99% confidence interval for the mean number of hours of TV teenage boys watch per day.
(b) Interpret the interval you found in part (a) in the context of the problem.

(c) If you were to construct a 99.5% confidence interval from the same data, would it be wider or narrower than the interval in part (a)?
(d) Construct an 88% confidence interval for the mean number of hours of TV teenage boys watch per day.
(e) Suppose we want to construct a 95% confidence interval for the mean number of hours of TV teenage boys watch per day, but we want our margin of error to be no more than 0.15 hours.
What is the smallest sample size we can use?
4. A consumer advocacy group is worried about the amount of sodium in sandwiches at a local fast food restaurant. They take a random sample of 100 sandwiches from a fast food restaurant and find a sample mean of 1042.7 milligrams. From previous studies they know the population standard deviation is 344.9 milligrams.
(a) Construct an 80% confidence interval for the mean sodium (in milligrams) amount in a sandwich.
(b) Interpret the confidence level in part (a) in the context of the problem
(c) If you were to construct an 84% confidence interval from the same data, would it be wider or narrower than the interval from (a)?

(d) Construct an 84% confidence interval for the mean sodium (in milligrams) amount in a sandwich.
(e) Suppose we want to construct a 90% confidence interval for the mean sodium (in milligrams) amount in a sandwich, but we want our margin of error to be no more than 25 milligrams. What is the smallest sample size we can use?