Statistics: A Tool For Social Research

Joseph F. Healey

Chapter 7 Estimation Procedures - all with Video Answers

Educators

Chapter Questions

06:07

Problem 1

For each set of sample outcomes below, construct the $95 \%$ confidence interval for estimating $\mu$, the population mean. $\begin{array}{rccc}\text { a. } \bar{X}=5.2 & \text { b. } \bar{X}=100 & \text { c. } \bar{X}=20 \\ s=0.7 & s=9 & s=3 \\ N=157 & N=620 & N=220 \\ \text { d. } \bar{X}=1020 & \text { e. } \bar{X}=7.3 & \text { f. } & \bar{X}=33 \\ s & =50 & s=1.2 & s & =6 \\ N=329 & N=105 & N=220\end{array}$

Sheryl Ezze

Numerade Educator

04:18

Problem 2

For each of the following sets of sample outcomes, construct the $99 \%$ confidence interval for estimating $P_{u}$.
a. $\begin{aligned} P_{s} &=0.40 \\ N &=548 \end{aligned}$
b. $\begin{aligned} P_{s} &=0.37 \\ N &=522 \end{aligned}$
c. $\begin{aligned} P_{s} &=0.79 \\ N &=121 \end{aligned}$
d. $\begin{aligned} P_{s} &=0.14 \\ N &=100 \end{aligned}$
e. $\begin{aligned} P_{s} &=0.43 \\ N &=1049 \end{aligned}$
f. $\begin{aligned} P_{s} &=0.63 \\ N &=300 \end{aligned}$

Sheryl Ezze

Numerade Educator

02:13

Problem 3

For each of the following confidence levels, determine the corresponding $Z$ score.
$$
\begin{array}{cccc}
\hline \begin{array}{c}
\text { Confidence } \\
\text { Level }
\end{array} & \text { Alpha } & \begin{array}{c}
\text { Area } \\
\text { Beyond } Z
\end{array} & Z \text { Score } \\
\hline 95 \% & 0.05 & 0.0250 & \pm 1.96 \\
94 \% & & & \\
92 \% & & & \\
97 \% & & & \\
98 \% & & & \\
\hline
\end{array}
$$

Sanchit Jain

Numerade Educator

01:40

Problem 4

You have developed a series of questions to measure job satisfaction of bus drivers in New York City. A random sample of 100 drivers has an average score of $10.6$, with a standard deviation of $2.8$. What is your estimate of the average job satisfaction score for the population as a whole? Use the $95 \%$ confidence level.

Maxime Rossetti

Numerade Educator

02:12

Problem 5

A researcher has gathered information from a random sample of 178 households. For each of the following variables, construct confidence intervals to estimate the population mean. Use the $90 \%$ level.
a. An average of $2.3$ people resides in each household. Standard deviation is $0.35$.
b. There was an average of $2.1$ television sets $(s=0.10)$ and $0.78$ telephones $(s=0.55)$ per household.
c. The households averaged $6.0$ hours of television viewing per day $(s=3.0)$

Adriano Chikande

Numerade Educator

01:54

Problem 6

A random sample of 100 HBO movies contained an average of $3.38$ acts of physical violence per program. At the $99 \%$ level, what is your estimate of the population value?
$$
\begin{aligned}
\bar{X} &=3.38 \\
s &=0.30 \\
N &=100
\end{aligned}
$$

Sheryl Ezze

Numerade Educator

04:32

Problem 7

A random sample of 429 college students was interviewed about a number of matters.
a. They reported that they had spent an average of $\$ 345.23$ on textbooks during the previous semester. If the sample standard deviation for these data is $\$ 15.78$, construct an estimate of the population mean at the $99 \%$ level.
b. They also reported that they had visited the health clinic an average of $1.5$ times a semester. If the sample standard deviation is $0.3$, construct an estimate of the population mean at the $99 \%$ level.
c. On the average, the sample had missed $2.8$ days of classes per semester because of illness. If the sample standard deviation is $1.0$, construct an estimate of the population mean at the $99 \%$ level.
d. On the average, the sample had missed $3.5$ days of classes per semester for reasons other than illness. If the sample standard deviation is $1.5, \mathrm{con}-$ struct an estimate of the population mean at the $99 \%$ level.

Nick Johnson

Numerade Educator

01:57

Problem 8

A random sample of 100 inmates at a maximum security prison shows that exactly 10 of the respondents had been the victims of violent crime during their incarceration. Estimate the proportion of victims for the population as a whole, using the $90 \%$ confidence level. (HINT: Calculate the sample proportion $P_{s}$ before using Formula 7.3. Remember that proportions are equal to frequency divided by $N$.)

Sheryl Ezze

Numerade Educator

02:42

Problem 9

The survey mentioned in problem $7.5$ found that 25 of the 178 households consisted of unmarried couples who were living together. What is your estimate of the population proportion? Use the $95 \%$ level.

Suman Saurav Thakur

Numerade Educator

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Problem 10

A random sample of } 260 \text { workers in a high-rise }\end{array}$ office building revealed that $30 \%$ were very satisfied with the quality of elevator service. At the $99 \%$ level, what is your estimate of the population value?

Kari Hasz

Numerade Educator

03:55

Problem 11

A random sample of 1496 respondents of a major metropolitan area was questioned about a number of issues. Construct estimates to the population at the $95 \%$ level for each of the results reported next. Express the final confidence interval in percentages (e.g., "between 40 and $45 \%$ agreed that premarital sex was always wrong").
a. When asked to agree or disagree with the statement "Explicit sexual books and magazines lead to rape and other sex crimes," 823 agreed.
b. When asked to agree or disagree with the statement "Hand guns should be outlawed," 650 agreed.
c. 375 of the sample agreed that marijuana should be legalized.
d. 1023 of the sample said that they had attended a church, synagogue, mosque, or other place of worship at least once within the past month.
e. 800 agreed that public elementary schools should have sex education programs starting in the fifth grade.

Sheryl Ezze

Numerade Educator

02:39

Problem 12

A random sample of 100 patients treated in a program for alcoholism and drug dependency over the past 10 years was selected. It was determined that 53 of the patients had been readmitted to the program at least once. At the $95 \%$ level, construct an estimate of the population proportion.

Andre Montanez Berrios

Numerade Educator

02:26

Problem 13

For the following sample data, construct five different interval estimates of the population mean, one each for the $90 \%, 95 \%, 99 \%, 99.9 \%$, and $99.99 \%$ levels. What happens to the interval width as confidence level increases? Why?
$$
\begin{aligned}
\bar{X} &=100 \\
s &=10 \\
N &=500
\end{aligned}
$$

Sheryl Ezze

Numerade Educator

05:07

Problem 14

For each of the following three sample sizes, construct the $95 \%$ confidence interval. Use a sample proportion of $0.40$ throughout. What happens to interval width as sample size increases? Why?
$$
\begin{aligned}
P_{s} &=0.40 \\
\text { Sample A: } N &=100 \\
\text { Sample B: } N &=1000 \\
\text { Sample C: } N &=10,000
\end{aligned}
$$

Sheryl Ezze

Numerade Educator

View

Problem 15

Two individuals are running for mayor of Shinbone. You conduct an election survey a week before the election and find that $51 \%$ of the respondents prefer candidate A. Can you predict a winner? Use the $99 \%$ level. (HINT: In a two-candidate race, what percentage of the vote would the winner need? Does the confidence interval indicate that candidate $A$ has a sure margin of victory? Remember that while the population parameter is probably $\alpha=0.01$ in the confidence interval, it may be anywhere in the interval.)
$$
\begin{aligned}
&P_{s}=0.51 \\
&N=578
\end{aligned}
$$

Danielle Fairburn

Numerade Educator

02:34

Problem 16

The World Values Survey is administered periodically to random samples from societies around the globe. Listed here are the number of respondents in each nation who said that they are "very happy." Compute sample proportions, and construct confidence interval estimates for each nation at the $95 \%$ level.
$$
\begin{array}{lcccc}
\hline \begin{array}{l}
\text { Nation }
\end{array} & \text { Year } & \begin{array}{c}
\text { Number } \\
\text { "Very } \\
\text { Happy" }
\end{array} & \begin{array}{c}
\text { Sample } \\
\text { Size }
\end{array} & \begin{array}{c}
\text { Confidence } \\
\text { Interval }
\end{array} \\
\hline \text { Great Britain } & 2006 & 528 & 1041 & \\
\text { Japan } & 2005 & 311 & 1096 & \\
\text { Brazil } & 2006 & 510 & 1500 & \\
\text { China } & 2007 & 424 & 2015 & \\
\text { Malaysia } & 2006 & 428 & 1201 & \\
\text { Mali } & 2007 & 598 & 1534 & \\
\text { Russia } & 2006 & 214 & 2033 &
\end{array}
$$

James Kiss

Numerade Educator

04:31

Problem 17

The fraternities and sororities at St. Algebra College have been plagued by declining membership over the past several years and want to know if the incoming freshman class will be a fertile recruiting ground. Not having enough money to survey all 1600 freshmen, they commission you to survey the interests of a random sample. You find that 35 of your 150 respondents are "extremely" interested in social clubs. At the $95 \%$ level, what is your estimate of the number of freshmen who would be extremely interested? (HINT: The high and low values of your final confidence interval are proportions. How can proportions also be expressed as numbers?)

Tony Wilson

Numerade Educator

02:36

Problem 18

You are the automotive specialist for the monthly magazine Consumer Beware. Part of your job is to investigate the claims made by automakers in their TV commercials. You are particularly suspicious of a new economy car that the automaker claims will get 78 miles per gallon. After checking the mileage figures for a random sample of 125 owners of this car, you find an average miles per gallon of $75.5$, with a standard deviation of $3.7$. At the $99 \%$ level, do your results tend to confirm or refute the manufacturer's claims?

Jerelyn Nevil

Numerade Educator

04:26

Problem 19

The results listed next are from a survey given to a random sample of the American public. For each sample statistic, construct a confidence interval estimate of the population parameter at the $95 \%$ confidence level. Sample size $(N)$ is 2987 throughout.
a. The average occupational prestige score was 43.87, with a standard deviation of $13.52$.
b. The respondents reported watching an average of $2.86$ hours of TV per day, with a standard deviation of $2.20$.
c. The average number of children was $1.81$, with a standard deviation of $1.67$.
d. Of the 2987 respondents, 876 identified themselves as Catholic.
e. Five hundred thirty-five of the respondents said that they had never married.
f. The proportion of respondents who said they voted for Bush in the 2004 presidential election was $0.52$.
g. When asked about capital punishment, 2425 of the respondents said that they favored the death penalty for murder.

Allen Sylvester

Numerade Educator