Topic 19 Practice Quiz
Suppose that you wanted to find out what proportion of students watch The Walking Dead on Netflix.
You take a sample of 110 students and find that 62 of them watch The Walking Dead.
a. Find the critical value, z*, for an 84% confidence interval.
b. Construct the 84% confidence interval by hand.
c. Find the critical value, z*, for a 97% confidence interval.
d. Construct the 97% confidence interval by hand.
e. How do the intervals in (b) and (d) compare and why?
f.
Suppose that you increased your sample size to 200, but the sample proportion remained the
same. How many students in this sample of 200 watch The Walking Dead?
g. By calculator, construct a 97% confidence interval for the sample of size 200.
h. What is the margin of error?
i.
How do the intervals in (d) and (g) compare and why?
j.
Explain, in context, what the 97% confidence interval from (g) means.
Topic 19 Practice Quiz Answers
Suppose that you wanted to find out what proportion of students watch The Walking Dead on Netflix.
You take a sample of 110 students and find that 62 of them watch The Walking Dead.
𝑝̂ =
62
= .5636
110
a. Find the critical value, z*, for an 84% confidence interval.
(100 – 84) /2 = 16 / 2 = 8  84% +8% = 92% =.92 = z* = 1.41
b. Construct the 84% confidence interval by hand.
.5636(1−.5636)
110
. 5636. ±1.41√
= (.4969, .6303)
c. Find the critical value, z*, for a 97% confidence interval.
(100 – 97)/2 = 3 / 2 = 1.5  97% +1.5% = 98.5% =.985 = z* = 2.17
d. Construct the 97% confidence interval by hand.
.5636(1−.5636)
110
. 5636. ±2.17√
= (.4609, .6662)
e. How do the intervals in (b) and (d) compare and why?
(d) is wider than (b) because the confidence level is larger
f.
Suppose that you increased your sample size to 200, but the sample proportion remained the
same. How many students in this sample of 200 watch The Walking Dead?
𝑝̂ = .5636. Since 𝑝̂ =
𝑥
𝑛
 x = 𝑝̂ 𝑛 = .5636 (200) = 112.72= 113 (round to 113 because we
cannot have a fraction of a person).
g. By calculator, construct a 97% confidence interval for the sample of size 200.
X= 113; n = 200; c-level = .97
By calculator: (.48893, .64107)
h. What is the margin of error?
.5636(1−.5636)
=
200
2.17√
i.
j.
.076097
How do the intervals in (d) and (g) compare and why?
(g) is narrower because g has a larger sample size.
Explain, in context, what the 97% confidence interval from (g) means.
We are 97% confident that between 49% and 64% of all students watch The Walking Dead on
Netflix.