# STATS HOMEWORK 8 ASSIGNMENT

Subject: Mathematics / Statistics
Question
Acid rain, caused by the reaction of certain air pollutants with rainwater, is a growing problem in the
United States. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity:
0 is acid? 14 is alkaline). Suppose water samples from 30 rainfalls are analyzed for pH, and x and s are
equal to 3.6 and 0.8, respectively. Find a 99% confidence interval for the mean pH in rainfall. (Round
3.200 to 4.032
Interpret the interval.
What assumption must be made for the confidence interval to be valid?
In repeated sampling, 99% of all intervals constructed in this manner will enclose the
population mean.
There is a 99% chance that an individual sample mean will fall within the interval.
In repeated sampling, 1% of all intervals constructed in this manner will enclose the population
mean.
99% of all values will fall within the interval.
There is a 1% chance that an individual sample mean will fall within the interval.
There must be at least 100 samples.
The sample must be random.
The sampling distribution must be symmetrical.
The sample mean must be greater than 5.
The standard deviation must be less than 10.

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state
of California. A random sample of 500 registrations are selected from a Department of Motor Vehicles
database, and 51 are classified as sports utility vehicles.
(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in
California. (Round your answers to three decimal places.)
.075 to .129
(b) How can you estimate the proportion of sports utility vehicles in California with a higher
degree of accuracy? (HINT: There are two answers. Select all that apply.)
increase the sample size n
increase z?/2 by increasing the confidence coefficient
decrease z?/2 by decreasing the confidence coefficient
conduct a non­random sample
decrease the sample size n

Independent random samples of size were selected from each of two populations. The
mean and standard deviations for the two samples were and
(a) Construct a 99% confidence interval for estimating the difference in the two population
means (Round your answers to two decimal places.)
to
(b) Does the confidence interval in part (a) provide sufficient evidence to conclude that there is a
difference in the two population means? Explain.
Since the value ?1 ? ?2 = 0 is in the confidence interval, it is not likely that there is a
difference in the population means.
Since the value ?1 ? ?2 = 0 is not in the confidence interval, it is likely that there is a
difference in the population means.
Since the value ?1 ? ?2 = 0 is in the confidence interval, it is likely that there is a
difference in the population means.
Since the value ?1 ? ?2 = 0 is not in the confidence interval, it is not likely that there is a
difference in the population means.
n1 = n2 = 100
x1 = 125.5, x2 = 123.9, s1 = 5.6,
s2 = 6.5.
(?1 ? ?2).\

Even within a particular chain of hotels, lodging during the summer months can vary substantially
depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing
statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and
record the nightly room rates. The means and standard deviations for 50 billing statements from each of
the computer databases of each of the three hotel chains are given in the table.
Hotel A Hotel B Hotel C
Sample Average (\$) 135 160 110
Sample Standard Deviation 17.2 22.3 12.8
(a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A
and the Hotel B chains. (Round your answers to two decimal places.)
\$ ­18.45 to \$ ­31.55
(b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B
and the Hotel C chains. (Round your answers to two decimal places.)
\$ 40.63 to \$ 59.37
(c) Do the intervals in parts (a) and (b) contain the value
Why is this of interest to the researcher?
(?1 ? ?2) = 0?
Yes, the interval in part (a) contains (?1 ? ?2) = 0.
Yes, the interval in part (b) contains (?1 ? ?2) = 0.
Yes, both intervals contain (?1 ? ?2) = 0.
No, neither interval contains (?1 ? ?2) = 0.
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(d) Do the data indicate a difference in the average room rates between the Hotel A and the
Hotel B chains?
Do the data indicate a difference in the average room rates between the Hotel B and the Hotel C
chains?
If (?1 ? ?2) = 0 is contained in the confidence interval, it is implied that the average
room rate for the two hotels was \$0.
If (?1 ? ?2) = 0 is contained in the confidence interval, it is implied that there is a
difference in the average room rates for the two hotels.
If (?1 ? ?2) = 0 is contained in the confidence interval, it is implied that there was an
error in the database records.
If (?1 ? ?2) = 0 is contained in the confidence interval, it is implied that there is no
difference in the average room rates for the two hotels.
If (?1 ? ?2) = 0 is contained in the confidence interval, it is implied that the room rate
for one of the hotels was \$0.
Yes, the data indicate a difference in the average room rates between the Hotel A and
the Hotel B chains.
No, the data do not indicate a difference in the average room rates between the Hotel
A and the Hotel B chains.
Yes, the data indicate a difference in the average room rates between the Hotel B and
the Hotel C chains.
No, the data do not indicate a difference in the average room rates between the Hotel
B and the Hotel C chains.

Independent random samples of and observations were selected from binomial
populations 1 and 2, and and successes were observed.
(a) Find a 90% confidence interval for the difference (p1 ? p2) in the two population proportions.
(Round your answers to three decimal places.)
.368 to ­284
Interpret the interval.
(b) What assumptions must you make for the confidence interval to be valid? (Select all that
apply.)
Are these assumptions met?
n1 = 600 n2 = 430
x1 = 332 x2 = 378
In repeated sampling, 90% of all intervals constructed in this manner will enclose the
true difference in population proportions.
In repeated sampling, 10% of all intervals constructed in this manner will enclose the
true difference in population proportions.
There is a 90% chance that an individual difference in sample proportions will fall
within the interval.
There is a 10% chance that an individual difference in sample proportions will fall
within the interval.
90% of all differences in the two population proportions will fall within the interval.
random samples
symmetrical distributions for both populations
nq > 5 for samples from both populations
np > 5 for samples from both populations
independent samples
n1 + n2 > 1000
Yes
No

In a study of the relationship between birth order and college success, an investigator found that 126 in
a sample of 180 college graduates were firstborn or only children. In a sample of 100 nongraduates of
comparable age and socioeconomic background, the number of firstborn or only children was 54.
Estimate the difference between the proportions of firstborn or only children in the two populations from
which these samples were drawn Use a 90% confidence interval. (Use p1 and p2 for the
proportions of firstborn or only children who were college graduates and nongraduates, respectively.
Round your answers to three decimal places.)
.061 to .260
(p1 ? p2).
90% of all proportions will fall within the interval.
There is a 10% chance that a single difference in sample proportions will fall within the
interval.
There is a 90% chance that a single difference in sample proportions will fall within the
interval.
In repeated sampling, 90% of all intervals constructed in this manner will enclose the true
value of p1 ? p2.
In repeated sampling, 10% of all intervals constructed in this manner will enclose the true
value of p1 ? p2.

Last year’s records of auto accidents occurring on a given section of highway were classified according
to whether the resulting damage was \$1000 or more and to whether a physical injury resulted from the
accident. The data follows.
Under \$1000 \$1000 or More
Number of Accidents 38 44
Number Involving Injuries 9 22
(a) Estimate the true proportion of accidents involving injuries when the damage was \$1000 or
more for similar sections of highway. (Round your answer to three decimal places.)
1.409
Find the 95% margin of error. (Round your answer to three decimal places.)
.160
(b) Estimate the true difference in the proportion of accidents involving injuries for accidents
with damage under \$1000 and those with damage of \$1000 or more. Use a 95% confidence
interval. (Round your answers to three decimal places.)
.771 to ­.067
12.0/2 points | Previous AnswersMendStat14 8.E.069.
Independent random samples of size 80 are drawn from two quantitative populations, producing the
sample information in the table. Find a 95% upper confidence bound for the difference in the two
population means (Round your answer to two decimal places.)
4.
Sample 1 Sample 2
Sample Size 80 80
Sample Mean 12 10
Sample Standard Deviation 7 8
(?1 ? ?2).
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13.2/2 points | Previous AnswersMendStat14 8.E.072.
Independent random samples of observations are to be selected from each of two
populations 1 and 2. If you wish to estimate the difference between the two population means correct to
within 0.16, with probability equal to 0.90, how large should n1 and n2 be? Assume that you know
(Round your answer up to the nearest whole number.)
14.0/2 points | Previous AnswersMendStat14 8.E.081.
Suppose you wish to estimate the difference between the mean acidity for rainfalls at two different
locations, one in a relatively unpolluted area and the other in an area subject to heavy air pollution. If
you wish your estimate to be correct to the nearest 0.2 pH, with probability near 0.90, approximately
how many rainfalls (pH values) would have to be included in each sample? (Assume that the variance of
the pH measurements is approximately 0.25 at both locations and that the samples will be of equal size.
Round your answer up to the nearest whole number.)
17 rainfalls
n1 = n2 = n
?1
2 ? ?2
2 ? 21.3.
n1 = n2 = 4530

A random sample of n = 49 observations has a mean x = 28.6 and a standard deviation s = 3.4.
(a) Give the point estimate of the population mean ?.
28.6
Find the 95% margin of error for your estimate. (Round your answer to four decimal places.)
.952
(b) Find a 90% confidence interval for ?. (Round your answers to three decimal places.)
27.801 to 29.399
What does “90% confident” mean?
(c) Find a 90% lower confidence bound for the population mean ?. (Round your answer to two
decimal places.)
27.9783
Why is this bound different from the lower confidence limit in part (b)?
In repeated sampling, 90% of all intervals constructed in this manner will enclose the
population mean.
There is a 10% chance that an individual sample mean will fall within the interval
limits.
There is a 90% chance that an individual sample mean will fall within the interval.
90% of all values will fall within the interval limits.
In repeated sampling, 10% of all intervals constructed in this manner will enclose the
population mean.
This bound is calculated using while the lower confidence limit in part (b) is
calculated using
This bound is calculated using n, while the lower confidence limit in part (b) is
calculated using
This bound is calculated using while the lower confidence limit in part (b) is
calculated using n.
This bound is calculated using while the lower confidence limit in part (b) is
calculated using
The lower bounds are based on different values of x.
z?/2,
z?.
n .
n ,
z?,
z?/2.

(d) How many observations do you need to estimate ? to within 0.4, with probability equal to
0.95? (Round your answer up to the nearest whole number.)
278 observations
16.2/5 points | Previous AnswersMendStat14 8.E.088.
A random sample of n = 500 observations from a binomial population produced x = 340 successes.
(a) Find a point estimate for p.
p? = .68
Find the 95% margin of error for your estimator. (Round your answer to three decimal places.)
.000
(b) Find a 90% confidence interval for p. (Round your answers to three decimal places.)
.679 to .681
Interpret this interval.
In repeated sampling, 10% of all intervals constructed in this manner will enclose the
population proportion.
In repeated sampling, 90% of all intervals constructed in this manner will enclose the
population proportion.
There is a 10% chance that an individual sample proportion will fall within the interval.
90% of all values will fall within the interval.
There is a 90% chance that an individual sample proportion will fall within the interval.

Independent random samples were selected from binomial populations 1 and 2. Suppose you wish to
estimate correct to within 0.01, with probability equal to 0.99, and you plan to use equal
sample sizes—that is, How large should n1 and n2 be? (Assume maximum variation. Round
your answer up to the nearest whole number.)
18.–/3 pointsMendStat14 8.E.094.
An experiment was conducted to estimate the effect of smoking on the blood pressure of a group of 31
cigarette smokers, by taking the difference in the blood pressure readings at the beginning of the
experiment and again 5 years later. The sample mean increase, measured in millimeters of mercury,
was and the sample standard deviation was Estimate the mean increase in blood
pressure that one would expect for cigarette smokers over the time span indicated by the experiment.
Find the 95% margin of error. (Round your answer to two decimal places.)
Describe the population associated with the mean that you have estimated.
The population is made up of the differences in blood pressure for all smokers and nonsmokers.
The population is made up of the differences in blood pressure for all smokers between the
beginning of the experiment and five years later.
The population is made up of the differences in blood pressure for all smokers and smokers over
40.
The population is made up of the differences in blood pressure for all smokers and nonsmokers
between the beginning of the experiment and five years later.
The population is made up of the differences in blood pressure for all smokers under 40 and
smokers over 40.
(p1 ? p2)
n1 = n2.
n1 = n2 =
x = 9.4, s = 5.5.
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19.–/3 pointsMendStat14 8.E.101.
Even though we know it may not be good for us, many Americans really enjoy their fast food! A survey
conducted by Pew Research Center graphically illustrated our penchant for eating out, and in particular,
eating fast food.
(a) This survey was based on “telephone interviews conducted with a nationally representative
sample of 2250 adults, ages 18 years and older, living in continental U.S. telephone households.”
What problems might arise with this type of sampling? (Select all that apply.)
wording bias
nonresponse
undercoverage
(b) How accurate do you expect the percentages given in the survey to be in estimating the
actual population percentages? (HINT: Find the 95% margin of error. Round your answer to three
decimal places.)
(c) If you want to decrease your margin of error to be ±1%, how large a sample should you
take? (Round your answer up to the nearest whole number.)

A dean of men wishes to estimate the average cost of the freshman year at a particular college correct
to within \$470, with a probability of 0.95. If a random sample of freshmen is to be selected and each
asked to keep financial data, how many must be included in the sample? Assume that the dean knows
only that the range of expenditures will vary from approximately \$14,800 to \$24,320. (Round your
answer up to the nearest whole number.)
freshmen
21.–/4 pointsMendStat14 8.E.111.
In addition to teachers and administrative staff, schools also have many other employees, including bus
drivers, custodians, and cafeteria workers. In Auburn, WA, the average hourly wage is \$16.92 for bus
drivers, \$17.65 for custodians, and \$12.86 for cafeteria workers. Suppose that a second school district
employs bus drivers who earn an average of \$14.75 per hour with a standard deviation of
Find a 95% confidence interval for the average hourly wage of bus drivers in school districts
similar to this one.
\$ to \$
Does your confidence interval enclose the Auburn, WA average of \$16.92?
Yes
No
What can you conclude about the hourly wages for bus drivers in this second school district?
Auburn, WA pays all workers significantly more per hour than the second school district pays.
Auburn, WA pays all workers significantly less per hour than the second school district pays.
Auburn, WA pays bus drivers significantly less per hour than the second school district pays.
Auburn, WA pays bus drivers significantly more per hour than the second school district pays.
No conclusion can be made based on the confidence interval.
n = 49
s = \$2.88.

In a study to establish the absolute threshold of hearing, 90 male college freshmen were asked to
participate. Each subject was seated in a soundproof room and a 150 H tone was presented at a large
number of stimulus levels in a randomized order. The subject was instructed to press a button if he
detected the tone? the experimenter recorded the lowest stimulus level at which the tone was detected.
The mean for the group was 22.1 db with s = 2.6. Estimate the mean absolute threshold for all college
freshmen.
Calculate the 95% margin of error. (Round your answer to two decimal places.)
23.–/2 pointsMendStat14 8.E.117.
A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a
sample should be taken if the grower wishes to estimate the proportion of his trees that are infected
with citrus red mite to within 0.05 with probability 0.95? (Round your answer up to the nearest whole
number.)
trees
24.2/2 points | Previous AnswersMendStat14 8.MC.002.
If you wish to construct 80% lower confidence bound (LCB) for the population mean ?, then the z­value
you should use is approximately:
a. .84
b. 2.58
c. 1.28
d. 2.33
e. 1.96