Basic Statistics for Business and Economics

Douglas A. Lind, William G. Marchal, Samuel A. Wathen

Chapter 11

Two-Sample Tests of Hypothesis - all with Video Answers

Educators

Chapter Questions

Problem 1

A sample of 40 observations is selected from one population. The sample mean is 102 and the sample standard deviation is $5 .$ A sample of 50 observations is selected from a second population. The sample mean is 99 and the sample standard deviation is $6 .$ Conduct the following test of hypothesis using the .04 significance level.
$$\begin{array}{l}H_{0}: \mu_{1}=\mu_{2} \\H_{1}: \mu_{1} \neq \mu_{2}\end{array}$$
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding $H_{0} ?$
e. What is the $p$ -value? Compute and interpret the $p$ -value.

Sheryl Ezze

Sheryl Ezze

Numerade Educator

Problem 2

A sample of 65 observations is selected from one population. The sample mean is 2.67 and the sample standard deviation is $0.75 .$ A sample of 50 observations is selected from a second population. The sample mean is 2.59 and the sample standard deviation is $0.66 .$ Conduct the following test of hypothesis using the .08 significance level.
$$\begin{array}{l}H_{0}: \mu_{1} \leq \mu_{2} \\H_{1}: \mu_{1}>\mu_{2}\end{array}$$
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding $H_{0} ?$
e. What is the $p$ -value? Compute and interpret the $p$ -value.

Sheryl Ezze

Numerade Educator

Problem 3

The Gibbs Baby Food Company wishes to compare the weight gain of infants using their brand versus their competitor's. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. The standard deviation of the sample was 2.3 pounds. A sample of 55 babies using the competitor's brand revealed a mean increase in weight of 8.1 pounds, with a standard deviation of 2.9 pounds. At the .05 significance level, can we conclude that babies using the Gibbs brand gained less weight? Compute the $p$ -value and interpret it.

Sheryl Ezze

Numerade Educator

Problem 4

As part of a study of corporate employees, the Director of Human Resources for PNC, Inc. wants to compare the distance traveled to work by employees at their office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month, with a standard deviation of 30 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month, with a standard deviation of 26 miles per month. At the .05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? Use the five-step hypothesis-testing procedure.

Sheryl Ezze

Numerade Educator

Problem 5

A financial analyst wants to compare the turnover rates, in percent, for shares of oil-related stocks versus other stocks, such as GE and IBM. She selected 32 oil-related stocks and 49 other stocks. The mean turnover rate of oil-related stocks is 31.4 percent and the standard deviation 5.1 percent. For the other stocks, the mean rate was computed to be 34.9 percent and the standard deviation 6.7 percent. Is there a significant difference in the turnover rates of the two types of stock? Use the .01 significance level.

Sheryl Ezze

Numerade Educator

Problem 6

Mary Jo Fitzpatrick is the Vice President for Nursing Services at St. Luke's Memorial Hospital. Recently she noticed that unionized jobs for nurses seem to offer higher wages. She decided to investigate and gathered the following sample information. Would it be reasonable for her to conclude that union nurses earn more? Use the .02 significance level. What is the $p$ -value? Compute and interpret the $p$ -value.

Sheryl Ezze

Numerade Educator

Problem 7

The null and alternate hypotheses are:
$H_{0}: \pi_{1} \leq \pi_{2}$
$H_{1}: \pi_{1}>\pi_{2}$
A sample of 100 observations from the first population indicated that $X_{1}$ is $70 .$ A sample of 150 observations from the second population revealed $X_{2}$ to be $90 .$ Use the .05 significance level to test the hypothesis.
a. State the decision rule.
b. Compute the pooled proportion.
c. Compute the value of the test statistic.
d. What is your decision regarding the null hypothesis?

Sheryl Ezze

Numerade Educator

Problem 8

The null and alternate hypotheses are:
$$\begin{array}{l}H_{0}: \pi_{1}=\pi_{2} \\H_{1}: \pi_{1} \neq \pi_{2}\end{array}$$
A sample of 200 observations from the first population indicated that $X_{1}$ is $170 .$ A sample of 150 observations from the second population revealed $X_{2}$ to be $110 .$ Use the .05 significance level to test the hypothesis.
a. State the decision rule.
b. Compute the pooled proportion.
c. Compute the value of the test statistic.
d. What is your decision regarding the null hypothesis?

Sheryl Ezze

Numerade Educator

Problem 9

The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod $5,$ and three others were sprayed with Action. When the grapes ripened, 400 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 400 vines sprayed with Action were checked. The results are: At the .05 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?

Sheryl Ezze

Numerade Educator

Problem 10

The Roper Organization conducted identical surveys in 1995 and $2005 .$ One question asked women was "Are most men basically kind, gentle, and thoughtful?" The 1995 survey revealed that, of the 3,000 women surveyed, 2,010 said that they were. In 2005,1,530 of the 3,000 women surveyed thought that men were kind, gentle, and thoughtful. At the .05 level, can we conclude that women think men are less kind, gentle, and thoughtful in 2005 compared with $1995 ?$

Sheryl Ezze

Numerade Educator

Problem 11

A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were: At the .02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards?

Sheryl Ezze

Numerade Educator

Problem 12

The research department at the home office of New Hampshire Insurance conducts ongoing research on the causes of automobile accidents, the characteristics of the drivers, and so on. A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three-year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the . 05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three-year period?

Sheryl Ezze

Numerade Educator

Problem 13

The null and alternate hypotheses are:
$$\begin{array}{l}H_{0}: \mu_{1}=\mu_{2} \\H_{1}: \mu_{1} \neq \mu_{2}\end{array}$$
A random sample of 10 observations from one population revealed a sample mean of 23 and a sample deviation of $4 .$ A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of $5 .$ At the .05 significance level, is there a difference between the population means?

Sheryl Ezze

Numerade Educator

Problem 14

The null and alternate hypotheses are:
$$\begin{array}{l}H_{0}: \mu_{1}=\mu_{2} \\H_{1}: \mu_{1} \neq \mu_{2}\end{array}$$
A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of $12 .$ A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of $15 .$ At the .10 significance level, is there a difference in the population means?

Sheryl Ezze

Numerade Educator

Problem 15

A sample of scores on an examination given in Statistics 201 are: At the .01 significance level, is the mean grade of the women higher than that of the men?

Sheryl Ezze

Numerade Educator

Problem 16

A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes. At the .01 significance level, can we conclude that the single-earner couples on average spend more time watching television together? There were 15 single-earner and 12 dual-earner couples studied.

Sheryl Ezze

Numerade Educator

Problem 17

Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information. At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the $p$ -value?

Sheryl Ezze

Numerade Educator

Problem 18

The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean weekly salary of nurses was larger than that of school teachers. To investigate, they collected the following information on the amounts earned last week by a sample of school teachers and nurses.

Sheryl Ezze

Numerade Educator

Problem 19

The null and alternate hypotheses are:
$$\begin{array}{l}H_{0}: \mu_{d} \leq 0 \\H_{1}: \mu_{d}>0\end{array}$$The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of four days last month. At the .05 significance level, can we conclude there are more defects produced on the afternoon shift?

Sheryl Ezze

Numerade Educator

Problem 20

The null and alternate hypotheses are:
$$\begin{array}{l}H_{0}: \mu_{d}=0 \\H_{1}: \mu_{d} \neq 0\end{array}$$
The following paired observations show the number of traffic citations given for speeding by Officer Dhondt and Officer Meredith of the South Carolina Highway Patrol for the last five months. At the .05 significance level, is there a difference in the mean number of citations given by the two officers?

Sheryl Ezze

Numerade Educator

Problem 21

The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded. Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the $p$ -value, and interpret it.

Sheryl Ezze

Numerade Educator

Problem 22

The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results. Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the $p$ -value.

Sheryl Ezze

Numerade Educator

Problem 23

A recent study focused on the number of times men and women who live alone buy takeout dinners in a month. The information is summarized below.
$$\begin{array}{|lcc|}\hline \text { Statistic } & \text { Men } & \text { Women } \\\hline \text { Mean } & 24.51 & 22.69 \\\text { Standard deviation } & 4.48 & 3.86 \\\text { Sample size } & 35 & 40 \\\hline\end{array}$$ At the .01 significance level, is there a difference in the mean number of times men and women order takeout dinners in a month? What is the $p$ -value?

Sheryl Ezze

Numerade Educator

Problem 24

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the afternoon shift than on the day shift. A sample of 54 day-shift workers showed that the mean number of units produced was $345,$ with a standard deviation of 21 . A sample of 60 afternoon-shift workers showed that the mean number of units produced was $351,$ with a standard deviation of 28 units. At the .05 significance level, is the number of units produced on the afternoon shift larger?

Sheryl Ezze

Numerade Educator

Problem 25

Fry Brothers Heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day, with a standard deviation of 1.05 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day, with a standard deviation of 1.23 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the $p$ -value?

Sheryl Ezze

Numerade Educator

Problem 26

A coffee manufacturer is interested in whether the mean daily consumption of regular coffee drinkers is less than that of decaffeinated-coffee drinkers. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day, with a standard deviation of 1.20 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.84 cups per day, with a standard deviation of 1.36 cups per day. Use the .01 significance level. Compute the $p$ -value.

Sheryl Ezze

Numerade Educator

Problem 27

A cell phone company offers two plans to it subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan $\mathrm{A}$ is $\$ 57,000$ with a standard deviation of $\$ 9,200 .$ This distribution is positively skewed; the actual coefficient of skewness is 2.11. For a sample of 30 subscribers to Plan B the mean income is $\$ 61,000$ with a standard deviation of $\$ 7,100 .$ The distribution of Plan B subscribers is also positively skewed, but not as severely. The coefficient of skewness is 1.54 . At the .05 significance level, is it reasonable to conclude the mean income of those selecting Plan $\mathrm{B}$ is larger? What is the $p$ -value? Do the coefficients of skewness affect the results of the hypothesis test? Why?

Sheryl Ezze

Numerade Educator

Problem 28

A computer manufacturer offers a help line that purchasers can call for help 24 hours a day 7 days a week. Clearing these calls for help in a timely fashion is important to the company's image. After telling the caller that resolution of the problem is important the caller is asked whether the issue is "software" or "hardware" related. The mean time it takes a technician to resolve a software issue is 18 minutes with a standard deviation of 4.2 minutes. This information was obtained from a sample of 35 monitored calls. For a study of 45 hardware issues, the mean time for the technician to resolve the problem was 15.5 minutes with a standard deviation of 3.9 minutes. This information was also obtained from monitored calls. At the . 05 significance level is it reasonable to conclude that it takes longer to resolve software issues? What is the $p$ -value?

Sheryl Ezze

Numerade Educator

Problem 29

The manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a sample of 200 current users is asked to try it. After a one-month trial, 180 indicated the new drug was more effective in relieving a headache. At the same time a sample of 300 current Advil users is given the current drug but told it is the new formulation. From this group, 261 said it was an improvement. At the .05 significance level can we conclude that the new drug is more effective?

Sheryl Ezze

Numerade Educator

Problem 30

Each month the National Association of Purchasing Managers publishes the NAPM index. One of the questions asked on the survey to purchasing agents is: Do you think the economy is expanding? Last month, of the 300 responses 160 answered yes to the question. This month, 170 of the 290 responses indicated they felt the economy was expanding. At the .05 significance level, can we conclude that a larger proportion of the agents believe the economy is expanding this month?

Sheryl Ezze

Numerade Educator

Problem 31

As part of a recent survey among dual-wage-earner couples, an industrial psychologist found that 990 men out of the 1,500 surveyed believed the division of household duties was fair. A sample of 1,600 women found 970 believed the division of household duties was fair. At the .01 significance level, is it reasonable to conclude that the proportion of men who believe the division of household duties is fair is larger? What is the $p$ -value?

Sheryl Ezze

Numerade Educator

Problem 32

There are two major Internet providers in the Colorado Springs, Colorado, area, one called HTC and the other Mountain Communications. We want to investigate whether there is a difference in the proportion of times a customer is able to access the Internet. During a oneweek period, 500 calls were placed at random times throughout the day and night to HTC. A connection was made to the Internet on 450 occasions. A similar one-week study with Mountain Communications showed the Internet to be available on 352 of 400 trials. At the .01 significance level, is there a difference in the percent of time that access to the Internet is successful?

Sheryl Ezze

Numerade Educator

Problem 33

The owner of Bun 'N' Run Hamburger wishes to compare the sales per day at two locations. The mean number sold for 10 randomly selected days at the Northside site was 83.55, and the standard deviation was $10.50 .$ For a random sample of 12 days at the Southside location, the mean number sold was 78.80 and the standard deviation was $14.25 .$ At the .05 significance level, is there a difference in the mean number of hamburgers sold at the two locations? What is the $p$ -value?

Sheryl Ezze

Numerade Educator

Problem 34

The Engineering Department at Sims Software, Inc., recently developed two chemical solutions designed to increase the usable life of computer disks. A sample of disks treated with the first solution lasted $86,78,66,83,84,81,84,109,65,$ and 102 hours. Those treated with the second solution lasted $91,71,75,76,87,79,73,76,79,78,87,90,76,$ and 72 hours. At the .10 significance level, can we conclude that there is a difference in the length of time the two types of treatment lasted?

Sheryl Ezze

Numerade Educator

Problem 35

The Willow Run Outlet Mall has two Gap Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of 10 customers at the Peach Street store revealed they spent the following amounts more than planned: $\$ 17.58, \$ 19.73, \$ 12.61, \$ 17.79, \$ 16.22, \$ 15.82, \$ 15.40, \$ 15.86, \$ 11.82,$ and $\$ 15.85 .$ A sample of 14 customers at the Plum Street store revealed they spent the following amounts more than they planned: $\$ 18.19, \$ 20.22, \$ 17.38, \$ 17.96, \$ 23.92, \$ 15.87$, $\$ 16.47, \$ 15.96, \$ 16.79, \$ 16.74, \$ 21.40, \$ 20.57, \$ 19.79,$ and $\$ 14.83 .$ At the .01 significance
level, is there a difference in the mean amounts purchased on impulse at the two stores?

Sheryl Ezze

Numerade Educator

Problem 36

The Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in the Little River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare the mean waiting time for patients at the two locations. Samples of the waiting times, reported in minutes, follow: At the .05 significance level, is there a difference in the mean waiting time?

Sheryl Ezze

Numerade Educator

Problem 37

The Commercial Bank and Trust Company is studying the use of its automatic teller machines (ATMs). Of particular interest is whether young adults (under 25 years) use the machines more than senior citizens. To investigate further, samples of customers under 25 years of age and customers over 60 years of age were selected. The number of ATM transactions last month was determined for each selected individual, and the results are shown below. At the .01 significance level, can bank management conclude that younger customers use the ATMs more?

Sheryl Ezze

Numerade Educator

Problem 38

Two boats, the Prada (Italy) and the Oracle (U.S.A.), are competing for a spot in the upcoming America's Cup race. They race over a part of the course several times. Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?

Sheryl Ezze

Numerade Educator

Problem 39

The manufacturer of an MP3 player wanted to know whether a 10 percent reduction in price is enough to increase the sales of their product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the sampled outlets. At the .01 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales?

Sheryl Ezze

Numerade Educator

Problem 40

A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. The numbers of minor accidents during a six-month period before and after the modifications were: At the .01 significance level is it reasonable to conclude that the modification reduced the number of traffic accidents?

Sheryl Ezze

Numerade Educator

Problem 41

Lester Hollar is Vice President for Human Resources for a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the $p$ -value.

Sheryl Ezze

Numerade Educator

Problem 42

The president of the American Insurance Institute wants to compare the yearly costs of auto insurance offered by two leading companies. He selects a sample of 15 families, some with only a single insured driver, others with several teenage drivers, and pays each family a stipend to contact the two companies and ask for a price quote. To make the data comparable, certain features, such as the amount deductible and limits of liability, are standardized. The sample information is reported below. At the .10 significance level, can we conclude that there is a difference in the amounts quoted?

Sheryl Ezze

Numerade Educator

Problem 43

Fairfield Homes is developing two parcels of land near Pigeon Fork, Tennessee. In order to test different advertising approaches, they use different media to reach potential buyers. The mean annual family income for 75 people making inquiries at the first development is $\$ 150,000,$ with a standard deviation of $\$ 40,000 .$ A corresponding sample of 120 people at the second development had a mean of $\$ 180,000,$ with a standard deviation of $\$ 30,000 .$ At the .05 significance level, can Fairfield conclude that the population means are different?

Sheryl Ezze

Numerade Educator

Problem 44

The following data resulted from a taste test of two different chocolate bars. The first number is a rating of the taste, which could range from 0 to $5,$ with a 5 indicating the person liked the taste. The second number indicates whether a "secret ingredient" was present. If the ingredient was present a code of "1" was used and a "0" otherwise. At the .05 significance level, does this data show a difference in the taste ratings?

Sheryl Ezze

Numerade Educator

Problem 45

An investigation of the effectiveness of an antibacterial soap in reducing operating room contamination resulted in the accompanying table. The new soap was tested in a sample of eight operating rooms in the greater Seattle area during the last year. At the .05 significance level, can we conclude the contamination measurements are lower after use of the new soap?

Sheryl Ezze

Numerade Educator

Problem 46

The following data on annual rates of return were collected from five stocks listed on the New York Stock Exchange ("the big board") and five stocks listed on NASDAQ. At the . 10 significance level, can we conclude that the annual rates of return are higher on the big board?

Sheryl Ezze

Numerade Educator

Problem 47

The city of Laguna Beach operates two public parking lots. The one on Ocean Drive can accommodate up to 125 cars and the one on Rio Rancho can accommodate up to 130 cars. City planners are considering both increasing the size of the lots and changing the fee structure. To begin, the Planning Office would like some information on the number of cars in the lots at various times of the day. A junior planner officer is assigned the task of visiting the two lots at random times of the day and evening and counting the number of cars in the lots. The study lasted over a period of one month. Below is the number of cars in the lots for 25 visits of the Ocean Drive lot and 28 visits of the Rio Rancho lot, Is it reasonable to conclude that there is a difference in the mean number of cars in the two lots? Use the .05 significance level.

Sheryl Ezze

Numerade Educator

Problem 48

The amount spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). An economist selected a sample of 20 homeowners in New England and then calculated these total housing costs as a percent of monthly income, five years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than five years ago?

Sheryl Ezze

Numerade Educator

Problem 49

Listed below are several prominent companies and their stock prices in June $2004 .$ Go to the Web and look up today's price. There are many sources to find stock prices, such as Yahoo and CNNFI. The Yahoo address is http://www.finance.yahoo.com. Enter the symbol identification to find the current price. At the .05 significance level, can we conclude that the prices have changed?

Carson Merrill

Numerade Educator

Problem 50

The USA Today Attp://www.usatoday.com/sports/baseball/front.htm) and Major League Baseball's fittp://www.majorleaguebaseball.com) websites regularly report information on individual player salaries in the American League and the National League. Go to one of these sites and find the individual salaries for your favorite team in each league. Compute the mean and the standard deviation. Is it reasonable to conclude that there is a difference in the salaries of the two teams?

Dominador Tan

Numerade Educator

Problem 51

Refer to the Real Estate data, which reports information on the homes sold in Denver, Colorado, last year.
a. At the .05 significance level, can we conclude that there is a difference in the mean selling price of homes with a pool and homes without a pool?
b. At the .05 significance level, can we conclude that there is a difference in the mean selling price of homes with an attached garage and homes without a garage?
c. At the .05 significance level, can we conclude that there is a difference in the mean selling price of homes in Township 1 and Township $2 ?$
d. Find the median selling price of the homes. Divide the homes into two groups, those that sold for more than (or equal to) the median price and those that sold for less. Is there a difference in the proportion of homes with a pool for those that sold at or above the median price versus those that sold for less than the median price? Use the .05 significance level.

Samuel Goyette

Numerade Educator

Problem 52

Refer to the Baseball 2003 data, which reports information on the 30 Major League Baseball teams for the 2003 season.
a. At the .05 significance level, can we conclude that there is a difference in the mean salary of teams in the American League versus teams in the National League?
b. At the .05 significance level, can we conclude that there is a difference in the mean home attendance of teams in the American League versus teams in the National League?
c. At the .05 significance level, can we conclude that there is a difference in the mean number of wins for teams that have artificial turf home fields versus teams that have grass home fields?
d. At the .05 significance level, can we conclude that there is a difference in the mean number of home runs for teams that have artificial turf home fields versus teams that have grass home fields?

Dominador Tan

Numerade Educator

Problem 53

Refer to the Wage data, which reports information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker.
a. Conduct a test of hypothesis to determine if there is a difference in the mean annual wages of southern residents versus nonsouthern residents.
b. Conduct a test of hypothesis to determine if there is a difference in the mean annual wages of white and nonwhite wage earners.
c. Conduct a test of hypothesis to determine if there is a difference in the mean annual wages of Hispanic and non-Hispanic wage earners.
d. Conduct a test of hypothesis to determine if there is a difference in the mean annual wages of female and male wage earners.
e. Conduct a test of hypothesis to determine if there is a difference in the mean annual wages of married and nonmarried wage earners.

Robin Corrigan

Numerade Educator

Problem 54

Refer to the CIA data, which reports demographic and economic information on 46 countries. Conduct a test of hypothesis to determine whether the mean percent of the population over 65 years of age in G20 countries is different from those that are not G20 members.

Victor Salazar

Numerade Educator