# STAT 200 Week 5 Homework Complete Solution

**Week**

5 Homework

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

Conclusion can you draw about this test of his ability to

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

this problem? Explain your choice.

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

this problem? Explain your choice.

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

exercises:

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

this problem? Explain your choice.

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?

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