Download Confidence Interval Quiz Review with Key - Washington

Confidence Level
80
90
95
99
Zc
1.28
1.645
1.96
2.575
Name: __________________________________________
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
21
13
17
21
14
17
22
14
18
22
15
18
22
15
18
22
15
18
23
16
19
24
16
19
24
16
19
24
16
20
24
16
21
25
The professor knows that the standard deviation of the number of credit hours taken by students
in her class is   3.5 hours.
(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?
4. 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?
5. 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?
Answer Key for Confidence Intervals – Quiz Review
1. (a) 54.5 minutes ; (b) E = 9.5
2. (a) 1443.69 < 𝜇 < 1566.31 ; (b) If you take samples of size 45, 90% of them will capture . ;
(c) It would be narrower because smaller confidence levels = smaller intervals ; (d) 1461.39 <
𝜇 < 1548.61 ; (e) 𝑛 ≥ 166
3. (a) 17.56 < 𝜇 < 19.84 ; (b) We are 95% confident that  is between 17.94 and 19.84. ; (c) The
confidence interval would be narrower since 82% is smaller than 95%. ; (d) 17.92 < 𝜇 < 19.48 ;
(e) 𝑛 ≥ 40
4. (a) 1.62 < 𝜇 < 2.22 ; (b) We are 99% confident that  is between 1.62 and 2.22. ; (c) The
confidence interval would be a bit wider since 99.5% is a little bigger than 99%. ; (d) 1.74 < 𝜇 <
2.10 ; (e) 𝑛 ≥ 68
5. (a) 998.55 < 𝜇 < 1086.85 ; (b) If you take samples of size 100, 80% of them will capture . ;
(c) The confidence interval would be wider since 84% is bigger than 80%. ; (d) 994.4 < 𝜇 <
1091 ; (e) 𝑛 ≥ 516