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mathematics
statistics

Elementary Statisitcs 2nd edition Barry Monk - Solutions

Polling results: A simple random sample of 400 voters in the town of East Overshoe was polled, and 242 said they planned to vote in favor of a bond issue to raise money for elementary schools. A simple random sample of 300 voters in West Overshoe was polled, and 161 said they were in favor.
Treating bean plants: In a study to measure the effect of an herbicide on the phosphate content of bean plants, a sample of 75 plants treated with the herbicide had a mean phosphate concentration (in percent) of 3.52 with a standard deviation of 0.41. and 100 untreated plants had a mean phosphate
Dueling scales: In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, ten rock specimens were weighed, in grams, on each scale. The following data were obtained:Construct a 98% confidence interval for mean difference in weight
Automobile pollution: In a random sample of 340 cars driven at low altitudes. 46 exceeded a threshold for the amount of particulate pollution. In a random sample of 85 cars driven at high altitudes. 21 exceeded a threshold for the amount of particulate pollution. Construct a 994 confidence interval
Why is it necessary for all values in the confidence interval to be positive to conclude that pi > P2? What would have to be true to conclude that pi < P2?
In what ways is the procedure for constructing a confidence interval for the difference between two proportions similar to constructing a confidence interval for one proportion? In what ways is it different?
For each health characteristic, construct a 95% confidence interval for the difference between the group means or group proportions.
Consider the evolution of wholesaling in relation to the evolution of retailing. List several changes that are similar, and several that are fundamentally different.
Do wholesalers and retailers need to worry about new product planning just as a producer needs to have an organized new-product development process? Explain your answer.
How do you think a retailer of Maytag washing machines would react if Maytag set up a website, sold direct to consumers, and shipped direct from its distribution center? Explain your thinking.
What is an agent wholesaler’s marketing mix?
Why do you think that many merchant wholesalers handle competing products from different producers, while manufacturers’ agents usually handle only noncompeting products from different producers?
What alternatives does a producer have if it is trying to expand distribution in a foreign market and finds that the best existing merchant wholesalers won’t handle imported products?
Discuss the future growth and nature of wholesaling if chains, scrambled merchandising, and the Internet continue to become more important. How will wholesalers have to adjust their mixes? Will wholesalers be eliminated? If not, what wholesaling functions will be most important? Are there any
What sort of a “product” are specialty shops offering? What are the prospects for organizing a chain of specialty shops?
Distinguish among discount houses, price-cutting by conventional retailers, and mass-merchandising. Forecast the future of low-price selling in food, clothing, and appliances. How will the Internet affect that future?
Discuss a few changes in the market environment that you think help to explain why telephone, mail-order, and Internet retailing have been growing so rapidly.
Apply the wheel of retailing theory to your local community. What changes seem likely? Will established retailers see the need for change, or will entirely new firms have to develop?
What advantages does a retail chain have over a retailer who operates with a single store? Does a small retailer have any advantages in competing against a chain? Explain your answer.
Many producers are now seeking new opportunities in international markets. Are the opportunities for international expansion equally good for retailers? Explain your answer.
Discuss how computer systems affect wholesalers’ and retailers’ operations.
Art Glass Productions, a producer of decorative glass gift items, wants to expand into a new territory. Managers at Art Glass know that unit sales in the new territory will be affected by consumer response to the products. But sales will also be affected by which combination of wholesalers and
A small company has developed an innovative new sprayon glass cleaner that prevents the buildup of electrostatic dust on computer screens and TVs. Give examples of some low-cost ways the firm might effectively promote its product. Be certain to consider both push and pull approaches.
Would promotion be successful in expanding the general demand for: (a) Almonds, (b) Air travel, (c) Golf clubs, (d) Walking shoes, (e) High-octane unleaded gasoline, (f) Single-serving, frozen gourmet dinners, (g) Bricks? Explain why or why not in each case.
Explain how an understanding of the adoption process would help you develop a promotion blend for digital tape recorders, a new consumer electronics product that produces high-quality recordings. Explain why you might change the promotion blend during the course of the adoption process.
Discuss how the adoption curve should be used to plan the promotion blend(s) for a new automobile accessory—an electronic radar system that alerts a driver if he or she is about to change lanes into the path of a car that is passing through a blind spot in the driver’s mirrors.
If a marketing manager uses the task method to budget for marketing promotions, are competitors’ promotion spending levels ignored? Explain your thinking and give an example that supports your point of view.
Discuss the potential conflict among the various promotion managers. How could this be reduced?
In your own words, discuss the integrated marketing communications concept. Explain what its emphasis on “consistent” and “complete” messages implies with respect to promotion blends.
Relate the three basic promotion objectives to the four jobs (AIDA) of promotion using a specific example.
Discuss the communication process in relation to a producer’s promotion of an accessory product—say, a new electronic security system businesses use to limit access to areas where they store confidential records.
If a company wants its promotion to appeal to a new group of target customers in a foreign country, how can it protect against its communications being misinterpreted?
Promotion has been the target of considerable criticism. What specific types of promotion are probably the object of this criticism? Give a particular example that illustrates your thinking.
With direct-response promotion, customers provide feedback to marketing communications. How can a marketing manager use this feedback to improve the effectiveness of the overall promotion blend?
How can a promotion manager target a message to a certain target market with electronic media (like the Internet) when the customer initiates the communication? Give an example.
What promotion blend would be most appropriate for producers of the following established products? Assume average- to large-sized firms in each case and support your answer.a. Chocolate candy bars.b. Car batteries.c. Panty hose.d. Castings for truck engines.e. A special computer used by
Helen Troy, owner of three Sound Haus stereo equipment stores, is deciding what message channel (advertising medium) to use to promote her newest store. Her current promotion blend includes direct-mail ads that are effective for reaching her current customers. She also has knowledgeable salespeople
A large company is considering a policy of flextime. in which employees can choose their own work schedules within broad limits. The company is interested to determine whether this policy would reduce the number of sick days taken. They chose two simple random samples of 100 employees each. The
The following MINITAB output presents a 95% confidence interval for the difference between two meana. Is this a left-tailed test, a right-tailed test, or a two-tailed test? b. How many degrees of freedom did the calculator use? c. What is the P-value? d. Can you reject Ho at the a = 0.05 level?
The following TI-84 plus calculator display Presents the results of a hypothesis test for the difference between two proportions. The sample sizes are n1 = 125 and n2 = 150a. Is this a left-tailed test, a right-tailed test. or a two-tailed test?b. What is the P-value?c. Can you reject Ho at the a
The following MINITAB output presents the results of a hypothesis test for the difference between two proportions.a. Is this a left-tailed test, a right-tailed test, or a two-tailed test?b. What is the P-value?c. Can you reject Ho at the a = 0.05 level?
The following TI-84 Plus calculator display presents the results of a hypothesis test for the mean difference between matched pairs.a. Is this a left-tailed test, a right-tailed test, or a two-tailed test?b. How many degrees of freedom are there?c. What is the P-value? d. Can you reject Ho at the a
The following output from MINITAB presents a confidence interval for the mean difference between matched pairs.a. Is this a left-tailed test, a right-tailed test or a two-tailed test? b. How many degrees of freedom are there? c. Can you reject H0 at the a = 0.05 level?
In a certain state, a referendum is being held to determine whether the transportation authority should issue additional highway bonds. A sample of 500 voters is taken in county A, and 285 say that they favor the bond proposal. A sample of 600 voters is taken in county b and 305 say that they favor
Contaminated water: The concentration of benzene was measured in units of milligrams per liter for a simple random sample of five specimens of untreated wastewater produced at a gas field. The sample mean was 7.8 with a sample standard deviation of 1.4. Seven specimens of treated wastewater had an
A company studied two programs for compensating its sales staff. Nine salespeople participated in the study. In program a sales people were paid a higher salary, plus a small commission for each item they sold. In program b they were paid a lower salary with a larger commission. Following are the
Medical researchers conducted a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication. which is pain caused by insufficient blood flow to the muscles of the legs. A sample of 8 patients walked on a treadmill for six minutes every
The General Social Survey reported in 2012 that in a sample of 68 men aged 18-25, the mean number of hours of television watched per day was 2.76 with a standard deviation of 2.21. In a sample of 72 women aged 18-25, the mean number of hours of television watched per day was 2.88 with a standard
An accounting firm tested two spreadsheet applications to determine whether there is a difference between them in the mean speed with which a standard accounting problem can be solved. The times needed for each of twelve accountants to solve the problem are as follows:Can you conclude that the mean
Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machinea. 960 met specifications regarding length and diameter. In a sample of 600 rods taken from machineb. 582 met the specifications. Machine B is more expensive to run, so it is decided
The following 11-84 Plus calculator display presents the results of a hypothesis test for the difference between two means. The sample sizes are n1 = 18 and n2 = 16.a. Is this a left-tailed test, a right-tailed test, or a two-tailed test? b. How many degrees of freedom did the calculator use? c.
Describe the differences between performing a hypothesis test for µ1-µ2 with paired samples and performing the same test for independent samples.
How do hypothesis tests for two population standard deviations differ from other tests presented in this chapter? In what ways are they similar?
Several null hypotheses are tested, and one of them is rejected after the Bonferroi adjustment. Explain why this null hypothesis would also have been rejected if it had been the only one tested.
For each of the five factors, test the null hypothesis that the population proportions are equal against the alternate hypothesis that they are not equal. Find the P-value for each test.
Null hypothesis: Let p0 be the probability that a family with four children has no boys, p 1 be the probability that a family has one boy, and so on. The null hypothesis is that the number of boys in a four- child family follows a binomial distribution with n = 4 and p = 0.5. State the null
Compute the expected frequencies under the null hypothesis of homogeneity.In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement, Some improvement, or
Test statistic: Compute the value of the chi- square statistic.In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement, Some improvement, or No
State a conclusion: Can you conclude that the distribution of outcomes differs among the hospitals? Use the . = 0.05 level of significance.In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome
Can€™t read the numbers: Because of printer failure, none of the observed frequencies in the following table were printed, but some of the row and column totals were. Is it possible to construct the corresponding table of expected frequencies from the information given? If so, construct
Powerball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. Between January 18, 2012, and June 26, 2013, a total of 755 balls numbered 1 through 59 were drawn. Following are the observed frequencies.Perform a test of the null
Absent from school: Following are the total numbers of absences on each day of the week for the academic year 2008€“ 2009 at a Montana elementary school.Test the null hypothesis that absences are equally likely to occur on any day of the week. Use the. = 0.05 level of significance.In a
Expected frequencies: Compute the expected frequencies. A hypothetical sample of 200 families, each with four children, was selected, and the number of boys was recorded for each. The results are presented in the following table.
Can you conclude that the distribution of boys differs from the binomial a hypothetical sample of 200 families, each with four children, was selected, and the number of boys was recorded for each. The results are presented in the following table.
Compute the expected frequencies under the null hypothesis of independence.The General Social Survey polled 1280 men and 1531 women to determine their level of education. The results are presented in the following table.
Compute the value of the chi- square statistic.The General Social Survey polled 1280 men and 1531 women to determine their level of education. The results are presented in the following table.
Can you conclude that education level is independent of gender? Use the. = 0.01 level of significance.The General Social Survey polled 1280 men and 1531 women to determine their level of education. The results are presented in the following table.
Compute the expected frequencies under the null hypothesis of homogeneity.In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement, Some improvement, or
Compute the value of the chi- square statistic.In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement, Some improvement, or No improvement. The results
Can you conclude that the quality varies among shifts? Use the. = 0.01 level of significance.In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement,
Why do large values of x2 provide evidence against H0? Why don’t small values of x2 provide evidence against H0?
Explain what the expected frequencies represent in a test of independence.
Use the data in Table 12.9 to test the null hypothesis that acceptance to graduate school is independent of gender. Show that this hypothesis is rejected at the . = 0.01 level.
Use the data in Table 12.10 to test the null hypothesis that acceptance to graduate school is independent of department. Show that this hypothesis is rejected at the . = 0.01 level.
Use the data in Table 12.11 to test the null hypothesis that gender is independent of department. Show that this hypothesis is rejected at the. = 0.01 level. We conclude that department is associated with both gender and admissions. Therefore, department is a confounder for the relationship between
For each department, test the hypothesis that gender and admissions are independent. Use the a = 0.01 level of significance. Show that the only department for which this hypothesis is rejected is department A. Show that, in fact, the admissions rate for women in department A is significantly higher
For each department, compute the proportion of all applicants who are accepted.
For each department, compute the proportion of all applicants who are men.
How's your mileage? Weight (in tons) and fuel economy (in mpg) were measured for a sample of seven diesel trucks. The results are presented in the following table.a. Compute the least-squares regression line for predicting mileage (y) from weight (x). b. Construct a 95% confidence interval for the
The following MINITAB output presents the results of a test of the null hypothesis Ho: A = 0.a. What are the slope and intercept of the least-squares regression line?b. Can you conclude that x is useful for predicting y? Use the a = 0.05 level of significance.
Following are measurements of particulate matter (PM) concentration (in micrograms per cubic meter), temperature, in degrees Fahrenheit, wind speed in miles per hour. and humidity in percent for 38 days in Denver, Colorado.a. Let y represent PM, x, represent temperature. x2 represent wind speed,
Following are data on maximum ice thickness in millimeters (y). average number of days per year of ice cover (xi). average number of days the bottom temperature is lower than 8°C (x2), and the average snow depth in millimeters (x3) for 13 lakes in Minnesota.b. Predict the ice thickness for a lake
Percentage of variation: The following MINITAB output presents a multiple regression equation.a. What percentage of the variation in the response is explained by the multiple regression equation? b. What percentage of the variation in the response is explained by the multiple regression equation,
The following MINITAB output presents a confidence interval for a mean response and a prediction interval for an individual response.a. Predict the value of y when xi = 2.5.x2 = 4.1, and x3 = 3.2. b. We are 95% confident that an individual whose values are xi = 2.5. x2 = 4.1. and x3 = 3.2 will
How's your mileage? Use the data in Exercise I for the following. a. Compute a point estimate for the mean mileage for trucks that weigh 20 tons. b. Construct a 95% confidence interval for the mean mileage of trucks that weigh 20 tons. c. Predict the mileage of a particular truck that weighs 20
How much wood is in that tree? For a sample of 12 trees the volume of lumber (in cubic meters) and the diameter (in centimeters) at a fixed height above ground level were measured. The results were as follows.a. Compute the least-squares regression line for predicting volume (y) from diameter
Use the data in Exercise 3 for the following. a. Compute a point estimate for the mean volume for trees with a diameter of 44 centimeters. b. Construct a 95 % confidence interval for the mean volume of trees with a diameter of 44 centimeters. c. Predict the volume for a particular tree whose
In tests designed to measure the effect of the concentration in percent of a certain additive on the drying time in hours of paint, the following data were obtained.a. Compute the least-squares regression line for predicting drying time (y) from concentration (.r).b. Construct a 95% confidence
Watching paint dry: Use the data in Exercise 5 for the following. a. Compute a point estimate for the mean drying time for paint with a concentration of 5.1. b. Construct a 95% confidence interval for the mean drying time for paint whose concentration is 5.1. c. Predict the mean drying time for a
Energy use: A sample of 10 households was monitored for one year. The household income (in $1000s) and the amount of energy consumed (in 101° joules) were determined. The results follow.a. Compute the least-squares line for predicting energy consumption (y) from income (x). b. Compute a 95%
Use the data in Exercise 7 for the following. a. Compute a point estimate for the mean energy use for families with an income of $50,000. b. Construct a 95% confidence interval for the mean energy use for families with an income of $50,000. c. Predict the energy use for a particular family with an
The following 11-84 Plus display presents the results of a test of the null hypothesis Ho: Î²1 = 0.a. What is the alternate hypothesis? b. What is the value of the test statistic? c. How many degrees of freedom are there?d. What is the P-value?e. Can you conclude that the explanatory variable is
The quantity ∑(x - )2 measures the spread in the x-values. Explain why using x-values that are more spread out will result in a narrower confidence interval for.
Suppose you are planning to buy a car that weighs 3500 pounds, and you have a linear model that predicts gas mileage (y) given the weight of the car (4. Which do you think would be more appropriate, a confidence interval for the mean gas mileage of cars that weigh 3500 pounds, or a prediction
Compute the least-squares regression line for predicting power (y) from wind speed (x).
Construct a residual plot and explain how it shows that the assumptions of the linear model are violated.
We cannot use the least-squares regression line to predict y from x. In these situations, statisticians often try to manipulate one or both of the variables to try to find a linear fit. This is called transforming the variables. For each data point, compute the cube of the wind speed to obtain x3,
Construct a residual plot to verify that the assumptions of the linear model are now satisfied.
Use the least-squares regression line computed in Exercise 3 to predict the power when the wind speed is 5.0 mph. (The value of the explanatory variable is 53 = 125.)
Soil quality: Soil scientists conducted an experiment in which the mineral gypsum was added in four different amounts to soil specimens to try to control the acid level of the soil. Three soil specimens received each amount added. The response variable is pH. which is a measurement of the acid

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