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Chapter 12: Q145SE (page 808)

Comparing private and public college tuition. According to the Chronicle of Higher Education Almanac, 4-year private colleges charge, on average, five times as much for tuition and fees than 4-year public colleges. In order to estimate the true difference in the mean amounts charged for an academic year, random samples of 40 private colleges and 40 public colleges were contacted and questioned about their tuition structures.

  1. Which of the procedures described in Chapter 8 could be used to estimate the difference in mean charges between private and public colleges?

  2. Propose a regression model involving the qualitative independent variable type of college that could be used to investigate the difference between the means. Be sure to specify the coding scheme for the dummy variable in the model.

  3. Explain how the regression model you developed in part b could be used to estimate the difference between the population means.

Short Answer

Expert verified

  1. The method of independent sampling to find the difference between two population means would be used here.

  2. The regression model can be written asEy= 尾0=尾1x1 where x1 denotes the type of college.

The estimated regression model developed in part b can be used to infer conclusions about the population means. When x1 = 1, Ey= 尾0+尾1and when x1 = 0 (meaning private college charges) which is taken as the base level here, E(y) = 尾0. Therefore, for x1 = 1, Ey= 尾0+尾1denotes the mean difference in the charges between private and public colleges.

Step by step solution

01

Difference between private and public college charges


The method of independent sampling to find the difference between two population means would be used here.

02

Regression model

Here to find a model indicating difference between means of private and public college charges a qualitative variable; x1; to denote the type of college is introduced where

X1= 1, if private college

0, if public college

The regression model can be written as Ey=尾0+尾1x1

03

Difference between population means

The estimated regression model developed in part b can be used to infer conclusions about the population means.

When x1= 1,Ey= 尾0+尾1 and when x1 = 0 (meaning private college charges) which is taken as the base level here, E (y) = 尾0

Therefore, for x1 = 1, Ey= 尾0+尾1denotes the mean difference in the charges between private and public colleges.

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Most popular questions from this chapter

Suppose the mean value E(y) of a response y is related to the quantitative independent variables x1and x2

E(y)=2+x1-3x2-x1x2

a) Identify and interpret the slope forx2

b) Plot the linear relationship between E(y) andx2for role="math" localid="1649796003444" x1=0,1,2, whererole="math" localid="1649796025582" 1鈮�x2鈮�3

c) How would you interpret the estimated slopes?

d) Use the lines you plotted in part b to determine the changes in E(y) for eachrole="math" localid="1649796051071" x1=0,1,2.

e) Use your graph from part b to determine how much E(y) changes whenrole="math" localid="1649796075921" 3鈮�x1鈮�5androle="math" localid="1649796084395" 1鈮�x2鈮�3.

Service workers and customer relations. A study in Industrial Marketing Management (February 2016) investigated the impact of service workers鈥� (e.g., waiters and waitresses) personal resources on the quality of the firm鈥檚 relationship with customers. The study focused on four types of personal resources: flexibility in dealing with customers(x1), service worker reputation(x2), empathy for the customer(x3), and service worker鈥檚 task alignment(x4). A multiple regression model was employed used to relate these four independent variables to relationship quality (y). Data were collected for n = 220 customers who had recent dealings with a service worker. (All variables were measured on a quantitative scale, based on responses to a questionnaire.)

a) Write a first-order model for E(y) as a function of the four independent variables. Refer to part

Which 尾 coefficient measures the effect of flexibility(x1)on relationship quality (y), independently of the other

b) independent variables in the model?

c) Repeat part b for reputation(x2), empathy(x3), and task alignment(x4).

d) The researchers theorize that task alignment(x4)鈥渕oderates鈥� the effect of each of the other x鈥檚 on relationship quality (y) 鈥� that is, the impact of eachx, x1,x2, orx3on y depends on(x4). Write an interaction model for E(y) that matches the researchers鈥� theory.

e) Refer to part d. What null hypothesis would you test to determine if the effect of flexibility(x1)on relationship quality (y) depends on task alignment(x4)?

f) Repeat part e for the effect of reputation(x2)and the effect of empathy(x3).

g) None of the t-tests for interaction were found to be 鈥渟tatistically significant鈥�. Given these results, the researchers concluded that their theory was not supported. Do you agree?

Question: Novelty of a vacation destination. Many tourists choose a vacation destination based on the newness or uniqueness (i.e., the novelty) of the itinerary. The relationship between novelty and vacationing golfers鈥� demographics was investigated in the Annals of Tourism Research (Vol. 29, 2002). Data were obtained from a mail survey of 393 golf vacationers to a large coastal resort in the south-eastern United States. Several measures of novelty level (on a numerical scale) were obtained for each vacationer, including 鈥渃hange from routine,鈥� 鈥渢hrill,鈥� 鈥渂oredom-alleviation,鈥� and 鈥渟urprise.鈥� The researcher employed four independent variables in a regression model to predict each of the novelty measures. The independent variables were x1 = number of rounds of golf per year, x2 = total number of golf vacations taken, x3 = number of years played golf, and x4 = average golf score.

  1. Give the hypothesized equation of a first-order model for y = change from routine.
  1. A test of H0: 尾3 = 0 versus Ha: 尾3< 0 yielded a p-value of .005. Interpret this result if 伪 = .01.
  1. The estimate of 尾3 was found to be negative. Based on this result (and the result of part b), the researcher concluded that 鈥渢hose who have played golf for more years are less apt to seek change from their normal routine in their golf vacations.鈥� Do you agree with this statement? Explain.
  1. The regression results for three dependent novelty measures, based on data collected for n = 393 golf vacationers, are summarized in the table below. Give the null hypothesis for testing the overall adequacy of the first-order regression model.
  1. Give the rejection region for the test, part d, for 伪 = .01.
  1. Use the test statistics reported in the table and the rejection region from part e to conduct the test for each of the dependent measures of novelty.
  1. Verify that the p-values reported in the table support your conclusions in part f.
  1. Interpret the values of R2 reported in the table.

Write a model that relates E(y) to two independent variables鈥攐ne quantitative and one qualitative at four levels. Construct a model that allows the associated response curves to be second-order but does not allow for interaction between the two independent variables.

Question: Write a regression model relating E(y) to a qualitative independent variable that can assume three levels. Interpret all the terms in the model.
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