# STAT 200 Week 5 Homework Complete Solution

Week
5 Homework

4. Why is a 99% confidence interval wider than a 95%
confidence interval?

12. A person claims to be able to
predict the outcome of flipping a coin. Thisperson is correct 16/25 times.
Compute the 95% confidence interval on theproportion of times this person can
predict coin flips correctly. What

predict the future?

15. You take a sample of 22 from a population of test
scores, and the mean of yoursample is 60. (a) You know the standard deviation
of the population is 10.What is the 99% confidence interval on the population
mean. (b) Now assumethat you do not know the population standard deviation, but
the standarddeviation in your sample is 10. What is the 99% confidence interval
on themean now?

18. You were interested in how long the average
psychology major at your collegestudies per night, so you asked 10 psychology
majors to tell you the amountthey study. They told you the following times: 2,
1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4.(a) Find the 95% confidence interval on the
population mean. (b) Find the 90%confidence interval on the population mean.

100. What
is meant by the term “90% confident” when constructing a confidence interval
for a mean?

a.
If we took repeated samples, approximately
90% of the samples would produce the same confidence interval.

b.
If we took repeated samples,
approximately 90% of the confidence intervals calculated from those samples
wouldcontain the sample mean.

c.
If we took repeated samples,
approximately 90% of the confidence intervals calculated from those samples
wouldcontain the true value of the population mean.

d.
If we took repeated samples, the
sample mean would equal the population mean in approximately 90% of thesamples.

106. Suppose
that a committee is studying whether or not there is waste of time in our
judicial system. It is interested inthe mean amount of time individuals waste
at the courthouse waiting to be called for jury duty. The committee
randomlysurveyed 81 people who recently served as jurors. The sample mean wait
time was eight hours with a sample standarddeviation of four hours.

a.

i.
x ¯ = __________

ii.
sx= __________

iii.
n= __________

iv.
n– 1 = __________

b.
Define the random variables X and X ¯ in words.

c.
Which distribution should you use for

d.
Construct a 95% confidence interval
for the population mean time wasted.

i.
State the confidence interval.

ii.
Sketch the graph.

iii.
Calculate the error bound.

112. In a
recent sample of 84 used car sales costs, the sample mean was \$6,425 with a
standard deviation of \$3,156. Assumethe underlying distribution is
approximately normal.

a.
Which distribution should you use for

b.
Define the random variable X ¯ in words.

c.
Construct a 95% confidence interval
for the population mean cost of a used car.

i.
State the confidence interval.

ii.
Sketch the graph.

iii.
Calculate the error bound.

d.
Explain what a “95% confidence
interval” means for this study.

Use the following information to answer the next two
exercises:
A quality control specialist for a
restaurant chain takes arandom sample of size 12 to check the amount of soda
served in the 16 oz. serving size. The sample mean is 13.30 with asample
standard deviation of 1.55. Assume the underlying population is normally
distributed.

116. What
is the error bound?

a.
0.87

b.
1.98

c.
0.99

d.
1.74

120. An
article regarding interracial dating and marriage recently appeared in the Washington Post.
Of the 1,709 randomlyselected adults, 315 identified themselves as Latinos, 323
identified themselves as blacks, 254 identified themselves asAsians, and 779
identified themselves as whites. In this survey, 86% of blacks said that they
would welcome a white personinto their families. Among Asians, 77% would
welcome a white person into their families, 71% would welcome a Latino,and 66%
would welcome a black person.

a.
We are interested in finding the 95%
confidence interval for the percent of all black adults who would welcome a

white
person into their families. Define the random variables X and P′, in
words.

b.
Which distribution should you use for

c.
Construct a 95% confidence interval.

i.
State the confidence interval.

ii.
Sketch the graph.

iii.
Calculate the error bound.

130. On
May 23, 2013, Gallup reported that of the 1,005 people surveyed, 76% of U.S.
workers believe that they willcontinue working past retirement age. The
confidence level for this study was reported at 95% witha 3%
margin of error.

a.
Determine the estimated proportion
from the sample.

b.
Determine the sample size.

c.
Identify CL and α.

d.
Calculate the error bound based on the
information provided.

e.
Compare the error bound in part d to
the margin of error reported by Gallup. Explain any differences between thevalues.

f.
Create a confidence interval for the
results of this study.

g.
A reporter is covering the release of
this study for a local news station. How should she explain the confidenceinterval
to her audience?