Homework 7

2.

PriviteraStats2 15.E.011.

State which correlation coefficient (Pearson, Spearman, point-biserial, or phi) should be used given the following information.

· Part (a)

Both factors are interval or ratio scale.

Pearson Spearman     point-biserial phi

· Part (b)

Both factors are ranked.

Pearson Spearman     point-biserial phi

· Part (c)

One factor is dichotomous and a second factor is continuous.

Pearson Spearman     point-biserial phi

· Part (d)

Both factors are dichotomous.

Pearson Spearman     point-biserial phi

PriviteraStats2 15.E.013.

State whether each of the following is an example of a positive or negative correlation.

· Part (a)

Higher education level is associated with a larger annual income.

positive correlation negative correlation    

· Part (b)

The smaller the class size, the more students believe they are receiving a quality education.

positive correlation negative correlation    

· Part (c)

Increased testosterone is associated with increased aggression.

positive correlation negative correlation    

· Part (d)

Rising prices of apples are associated with the sale of fewer apples.

positive correlation negative correlation    

PriviteraStats2 15.E.017.

A medical study found a negative relationship between exercise (in minutes per week) and stress-related heath problems

(r = −0.36).

Which of the following conclusions is appropriate? Explain why the other is not appropriate.

(a) 12.96% of the variance in stress-related health problems can be explained by the amount of weekly exercise. (b) Increasing the amount of exercise per week will cause stress-related health problems to decrease.

Conclusion (b) is appropriate. Conclusion (a) is not appropriate because the amount of variance that can be explained is 36%.

Conclusion (a) is appropriate. Conclusion (b) is not appropriate because correlations do not demonstrate cause.    

  Conclusion (a) is appropriate. Conclusion (b) is not appropriate because increasing the amount of exercise per week will cause stress-related health problems to also increase.

Conclusion (b) is appropriate. Conclusion (a) is not appropriate because it is impossible to determine the variance in stress-related health problems that can be explained by the amount of weekly exercise.

5.

PriviteraStats2 15.E.019.

A researcher measures the relationship between sleep medication use (times used per week) and time spent working (in hours per week). Answer the following questions based on the results provided.

· Part (a)

Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)

· Part (b)

Multiply each measurement of drug use times 3 and recalculate the correlation coefficient. (Round your answer to three decimal places.)

· Part (c)

Divide each measurement in half for time spent working and recalculate the correlation coefficient. (Round your answer to three decimal places.)

· Part (d)

True or false: Multiplying or dividing a positive constant to one set of scores (X or Y) does not change the correlation coefficient. Note: Use your answers in (a) to (c) to answer true or false.

True False    

PriviteraStats2 15.E.021.

A therapist specializing in family counseling measures the relationship between partners and marital satisfaction. Husbands and wives rated how satisfied they were in their marriage using a 7-point rating scale ranging from 1 (not satisfied at all) to 7 (very satisfied). Using the hypothetical data given in the following table, compute the Pearson correlation coefficient. (Round your answer to three decimal places.)

PriviteraStats2 15.E.023.

A researcher measures the relationship between Internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.

(a) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.) (b) Compute the coefficient of determination. (Round your answer to three decimal places.) (c) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.

Retain the null hypothesis. Reject the null hypothesis.    

PriviteraStats2 15.E.025.

Using the Pearson correlation coefficient, researchers studying the dangers of cell phone use while driving found a positive correlation between cell phone use while driving and car accidents

(r = 0.16)

in a sample of 37 participants. Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.

Retain the null hypothesis. Reject the null hypothesis.    

9.

PriviteraStats2 15.E.027.

Employers often use standardized measures to gauge how likely it is that a new employee with little to no experience will succeed in their company. One such factor is intelligence, measured using the Intelligence Quotient (IQ). To show that this factor is related to job success, an organizational psychologist measures the IQ score and job performance (in units sold per day) in a sample of 10 new employees.

(a) Convert the following data to ranks and then compute a Spearman correlation coefficient. (Round your answer to three decimal places.) (b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.

Retain the null hypothesis. Reject the null hypothesis.    

PriviteraStats2 15.E.029.

To test whether extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

(a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.) (b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis. Hint: You must first convert r to a t-statistic.

Retain the null hypothesis. Reject the null hypothesis.    

PriviteraStats2 15.E.031.

A therapist measures the relationship between a patient's expectations that therapy will be successful and the actual success of the therapy. The following table shows the results of this hypothetical study using a sample of 50 clients.

(a) Compute the phi correlation coefficient. (Round your answer to three decimal places.) (b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis. Hint: You must first convert r to χ2.

Retain the null hypothesis. Reject the null hypothesis.    

PriviteraStats2 15.E.033.

Nobre and Pinto-Gouveia (2008) measured the relationship between emotion and thoughts of low self-body image. The following table shows a portion of their results for the correlations between thoughts of low-self body image and four types of emotions.

(a) List the emotions that showed a significant positive correlation with thoughts of low self-body image. (Select all that apply.)

guilt satisfaction sadness pleasure

(b) List the emotions that showed a significant negative correlation with thoughts of low self-body image. (Select all that apply.)

pleasure sadness guilt satisfaction

PriviteraStats2 16.E.001.

State the equation of the regression line used to predict values of the criterion variable.

X = bY + a

Y = bX + se

X = bY + se

Y = bX + a

Y = MY − bMx

14.

PriviteraStats2 16.E.013.

Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?

· Part (a)

A researcher tests whether the size of an audience can predict the number of mistakes a student makes during a classroom presentation. Identify the predictor variable.

number of presentations size of classrooms     size of audience number of mistakes

Identify the criterion variable.

number of mistakes size of classrooms     size of audience number of presentations

· Part (b)

A social psychologist tests whether the size of a toy in cereal boxes can predict preferences for that cereal. Identify the predictor variable.

liking for the cereal size of a toy in a cereal box     size of cereal boxes liking for the toy

Identify the criterion variable.

size of cereal boxes size of a toy in a cereal box     liking for the cereal liking for the toy

· Part (c)

A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas. Identify the predictor variable.

troop morale number of troops     duration of good morale duration of overseas tour

Identify the criterion variable.

duration of good morale number of troops     duration of overseas tour troop morale

PriviteraStats2 16.E.015.

For each of the following regression equations, explain how the criterion variable (Y) changes as the predictor variable (X) increases. Hint: You can find the answer by looking at the equation.

(a)    

= 0.96X − 2.80

The criterion variable increases. The criterion variable decreases.     The criterion variable remains the same.

(b)    

= −3.01X − 0.90

The criterion variable increases. The criterion variable decreases.     The criterion variable remains the same.

(c)    

= 8.90X + 11

The criterion variable increases. The criterion variable decreases.     The criterion variable remains the same.

(d)    

= −9.72X + 17

The criterion variable increases. The criterion variable decreases.     The criterion variable remains the same.

16.

PriviteraStats2 16.E.017.

An animal trainer tests whether the number of hours of obedience training can predict where a dog places in a dog show. The hypothetical data are given below.

In terms of the method of least squares, which of the following regression lines is the best fit for these data?

= 0.318X − 7.140

= −1.3X − 4.75

= −0.318X + 7.140

= 1.3X + 4.75

PriviteraStats2 16.E.019.

A forensic psychologist tests the extent to which the age of a criminal (X) predicts the age of the victim (Y) for nonviolent crimes. The psychologist uses the case files to record the age of five criminals and the age of the victim in those cases. The hypothetical data are listed in the following table.

(a) Compute the method of least squares to find the equation of the regression line. (Round your answers to three decimal places.) = X + (b) Use the regression equation to determine the predicted age of a victim of a nonviolent crime when the criminal is 23 years old. (Round your answer to three decimal places.) years old

18.

PriviteraStats2 16.E.021.

An instructor measured quiz scores and the number of hours studying among a sample of 20 college students. If

SSXY = 48,

SSX = 98,

MY = 7,

and

MX = 5,

then what is the regression equation for this sample? (Round your numerical values to three decimal places.) = X +

PriviteraStats2 16.E.023.

A researcher tested whether time of day could predict mood in a sample of 16 college students. If

SSresidual = 350,

then what is the standard error of estimate in this sample?

PriviteraStats2 16.E.025.

A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table.

Compute an analysis of regression for this hypothetical study. (Round your answers to two decimal places.)

Make a decision to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

Retain the null hypothesis. Reject the null hypothesis.    

PriviteraStats2 16.E.027.

A sports psychologist tested whether the number of team wins in the previous season can predict the number of wins in the following season in a sample of 35 teams. Complete the regression table for this hypothetical study. (Round your value for Fobt to two decimal places.)

Make a decision to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

Retain the null hypothesis. Reject the null hypothesis.