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Chapter 12: Q27E (page 732)

Question: Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on one鈥檚 desire to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that psychologists used multiple regression to model desire to have cosmetic surgery (y) as a function of gender(x1) , self-esteem(x2) , body satisfaction(x3) , and impression of reality TV (x4). The SPSS printout below shows a confidence interval for E(y) for each of the first five students in the study.

  1. Interpret the confidence interval for E(y) for student 1.
  2. Interpret the confidence interval for E(y) for student 4

Short Answer

Expert verified

(a) The confidence interval for E(y) for student 1 here is (13.42, 14.31) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (13.42, 14.31) for student 1.

(b) The confidence interval for E(y) for student 4 here is (8.79, 10.89) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (8.79, 10.89) for student 4.

Step by step solution

01

Step-by-Step SolutionStep 1: Interpretation of confidence interval for the population mean

Student 1鈥檚 desire to have cosmetic surgery can be computed at 11. The confidence interval for E(y) for student 1 here is (13.42, 14.31) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (13.42, 14.31) for student 1.

02

Explanation of confidence interval for the population mean

Student 4鈥檚 desire to have cosmetic surgery is represented as 11. The confidence interval for E(y) for student 4 here is (8.79, 10.89) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (8.79, 10.89) for student 4

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Most popular questions from this chapter

Question: Suppose you fit the interaction model y=尾0+尾1x1+尾2x2+尾3x1x2+蔚 to n = 32 data points and obtain the following results:SSyy=479,鈥�SSE=21,鈥�尾^3=10, and s尾^3=4

a. Find R2and interpret its value.

b. Is the model adequate for predicting y? Test at 伪=.05

c. Use a graph to explain the contribution of the x1 , x2 term to the model.

d. Is there evidence that x1and x2 interact? Test at 伪=.05 .

Consider relating E(y) to two quantitative independent variables x1 and x2.

  1. Write a first-order model for E(y).

  2. Write a complete second-order model for E(y).

It is desired to relate E(y) to a quantitative variable x1and a qualitative variable at three levels.

  1. Write a first-order model.

  2. Write a model that will graph as three different second- order curves鈥攐ne for each level of the qualitative variable.

Question: Shared leadership in airplane crews. Refer to the Human Factors (March 2014) study of shared leadership by the cockpit and cabin crews of a commercial airplane, Exercise 8.14 (p. 466). Recall that simulated flights were taken by 84 six-person crews, where each crew consisted of a 2-person cockpit (captain and first officer) and a 4-person cabin team (three flight attendants and a purser.) During the simulation, smoke appeared in the cabin and the reactions of the crew were monitored for teamwork. One key variable in the study was the team goal attainment score, measured on a 0 to 60-point scale. Multiple regression analysis was used to model team goal attainment (y) as a function of the independent variables job experience of purser (x1), job experience of head flight attendant (x2), gender of purser (x3), gender of head flight attendant (x4), leadership score of purser (x5), and leadership score of head flight attendant (x6).

a. Write a complete, first-order model for E(y) as a function of the six independent variables.

b. Consider a test of whether the leadership score of either the purser or the head flight attendant (or both) is statistically useful for predicting team goal attainment. Give the null and alternative hypotheses as well as the reduced model for this test.

c. The two models were fit to the data for the n = 60 successful cabin crews with the following results: R2 = .02 for reduced model, R2 = .25 for complete model. On the basis of this information only, give your opinion regarding the null hypothesis for successful cabin crews.

d. The p-value of the subset F-test for comparing the two models for successful cabin crews was reported in the article as p 6 .05. Formally test the null hypothesis using 伪 = .05. What do you conclude?

e. The two models were also fit to the data for the n = 24 unsuccessful cabin crews with the following results: R2 = .14 for reduced model, R2 = .15 for complete model. On the basis of this information only, give your opinion regarding the null hypothesis for unsuccessful cabin crews.

f. The p-value of the subset F-test for comparing the two models for unsuccessful cabin crews was reported in the article as p < .10. Formally test the null hypothesis using 伪 = .05. What do you conclude?

Question: Personality traits and job performance. Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.54 (p. 747). Recall that the researchers used a quadratic model to relate y = task performance score (measured on a 30-point scale) to x1 = conscientiousness score (measured on a scale of -3 to +3). In addition, the researchers included job complexity in the model, where x2 = {1 if highly complex job, 0 if not}. The complete model took the form

E(y)=尾0+尾1x1+尾2x12+尾3x2+尾4x1x2+尾5x12x2herex2=1E(y)=尾0+尾1x1+尾2x12+尾3(1)+尾4x1(1)+尾5(1)2(1)E(y)=(尾0+尾3)+(尾1+尾4)x1+(尾2+尾5)(x1)2

a. For jobs that are not highly complex, write the equation of the model for E1y2 as a function of x1. (Substitute x2 = 0 into the equation.)

b. Refer to part a. What do each of the b鈥檚 represent in the model?

c. For highly complex jobs, write the equation of the model for E(y) as a function of x1. (Substitute x2 = 1 into the equation.)

d. Refer to part c. What do each of the b鈥檚 represent in the model?

e. Does the model support the researchers鈥� theory that the curvilinear relationship between task performance score (y) and conscientiousness score (x1) depends on job complexity (x2)? Explain.
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