16.9 Price Discrimination?

CASE 16.1 In Examples 16.1 through 16.4, the testing of significance was based on the rank sum of the Used Auto consumers being the first group. Suppose we associate the first group with the Midwest Auto consumers. As noted in the section (page 16-5), the rank sum for Midwest Auto consumers is 55.

16.10 Wheat prices.

Example 7.13 (pages 385-386) reports the results of a small survey that asked separate samples of 5 wheat producers in each of January and July what price they received for wheat sold that month. Here are the data:

The stemplot on page 386 shows a large difference between months. We cannot assess Normality from such small samples. Carry out by hand the steps in the Wilcoxon rank sum test for comparing prices in January and July.

16.11 Online discussion posting.

Students in a fully online MBA statistics course are required as to post relevant learning contributions in the course’s discussion forum throughout the semester. These posts serve as a form of online participation and factor into their grades. Below find the number of posts during the semester by the six female students in the class.⁵

Find the ranks for these data.

16.12 Find the rank sum statistic.

Refer to the previous exercise. Here are the data for the 10 men in the class.

Compute the value of the Wilcoxon statistic. Take the first sample to be the women.

16.13 State the hypotheses.

Refer to the previous exercise. State appropriate null and alternative hypotheses for this setting.

16.14 Find the mean and standard deviation of the distribution of the statistic.

The statistic that you calculated in Exercise 16.12 is a random variable with a sampling distribution. What are the mean and the standard deviation of this sampling distribution under the null hypothesis?

16.15 Find the -value.

Refer to Exercises 16.11 through 16.14. Find the -value using the Normal approximation with the continuity correction and interpret the result of the significance test.

16.16 Counts of seeds in one-pound scoops.

Exercise 7.55 (page 395) discusses a study of two different packaging plants in terms of the packaging of seeds. An SRS of 50 one-pound scoops of seeds was collected from Plant 1746, and an SRS of 19 one-pound scoops of seeds was collected from Plant 1748. The number of seeds found in each scoop was recorded. Histograms and Normal quantile plots suggest the data arise from non-Normal distributions. Using software, is there a significant difference in the number of seeds per pound between the two plants based on the Wilcoxon test?

16.17 Polyester fabrics in landfills.

How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay. Lower strength means the fabric has decayed. Part of the study involved burying 10 polyester strips in well-drained soil in the summer. Five of the strips, chosen at random, were dug up after two weeks; the other five were dug up after 16 weeks. Here are the breaking strengths in pounds:⁶

16.18 Economic growth.

The most commonly used measure of economic growth is the rate of growth in a country’s total output of goods and services gauged by the gross domestic product (GDP) adjusted for inflation. The level of a country’s GDP growth reflects on the growth of businesses, jobs, and personal income. Here are World Bank data on the average growth of GDP (percent per year) for the period 2010 to 2013 in developing countries of Europe:⁷

Here are the data for nearby developing countries of the Central Asia:

16.19 It’s your choice.

Exercise 16.18 asks for the rank sum for Central Asia.

16.20 ERP implementation.

Companies worldwide are investing in enterprise resource planning (ERP) systems. ERP is an integrated business management software system that allows companies to share common data across all functional business areas. By linking areas of a company with a single system, the premise is that companies will reduce costs and improve efficiencies corporate-wide. In a study, researchers investigated if ERP implementation had positive impact on facility management (FM) services. A survey was conducted on companies with and without ERP systems. Data were collected by company on the number of FM-related areas that have had productivity improvements in the given calendar year. The researchers were interested in testing the alternative hypothesis that the number of FM-related productivity improvements was greater for ERP companies than non-ERP companies.⁸

16.21 The influence of subliminal messages.

Can “subliminal” messages that are below our threshold of awareness nonetheless influence us? Advertisers, among others, want to know. One study asked if subliminal messages help students learn math. A group of students who had failed the mathematics part of the City University of New York Skills Assessment Test agreed to participate in a study to find out. All received a daily subliminal message, flashed on a screen too rapidly to be consciously read. The treatment group of 10 students was exposed to “Each day I am getting better in math.” The control group of eight students was exposed to a neutral message, “People are walking on the street.” All students participated in a summer program designed to raise their math skills, and all took the assessment test again at the end of the program. Here are data on the subjects’ scores before and after the program.⁹

16.22 Fitness and ego.

Exercise 7.63 describes a study of fitness and personality. In particular, 28 middle-aged college faculty were evenly divided into low-fitness and high-fitness groups. The subjects then took the Cattell Sixteen Personality Factor Questionnaire. The provided data are the measurements of “ego strength.”

16.23 Safety of restaurant food.

CASE 16.2 Case 16.2 (page 16-10) describes a study of the attitudes of people attending outdoor fairs about the safety of the food served at such locations. In the associated data file, you will find the responses of 303 people to several questions. The variables in this data set are (in order)

The variable “sfair” contains the responses described in the example concerning safety of food served at outdoor fairs and festivals. The variable “srest” contains responses to the same question asked about food served in restaurants. We saw that women are more concerned than men about the safety of food served at fairs. Is this also true for restaurants?

16.24 Food safety at fairs and in restaurants.

CASE 16.2 The data file used in Example 16.5 (page 16-11) and Exercise 16.23 contains 303 rows, one for each of the 303 respondents. Each row contains the responses of one person to several questions. We wonder if people are more concerned about the safety of food served at fairs than they are about the safety of food served at restaurants. Explain carefully why we cannot answer this question by applying the Wilcoxon rank sum test to the variables “sfair” and “srest.”

16.25 Sadness and spending.

Exercise 7.52 (page 394) studies the effect of sadness on a person’s spending judgment. In the exercise, we find 17 participants in the sad group and 14 participants in the neutral group.

16.26 Patient satisfaction.

A Wisconsin health care provider has a network of hospitals serving communities throughout eastern Wisconsin. In an attempt to continually improve its services, this provider conducts patient and employee satisfaction surveys. To measure overall rating of a given hospital, patients are asked, “Would you recommend this hospital to your friends and family?” Answer choices are definitely no, probably no, probably yes, definitely yes. The responses are coded numerically from 1 to 4. Here are quarterly survey data for one of its urban-based hospitals and for one of its suburban-based hospitals.