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PSYC 2317 – Introduction to Statistical Methods

Computational Exam #2

Computations: Read each problem scenario carefully and do the calculations systematically. To ensure credit, partial or otherwise, show all your work.

Write the formula(s) first, plug in the values, and solve. Please write legibly. Some problems require you to write your answer in the boxes provided.

1. A cognitive psychologist was interested in the relationship between motivation scores and

performance. She administered a motivation questionnaire (a higher score indicates higher levels of motivation) to 5 participants and then gave them a task to perform. Performance was based on the number of correct responses on the task. Using the data shown below, draw a scatterplot and visually estimate the location of the regression line as well as you can (draw it). (5 pts)

Participant # Motivation Score # of correct responses

#1 8 3

#2 12 10

#3 9 6

#4 6 8

# 5 5 7

2. Determine mathematically the strength and direction of the relationship between motivation scores and the number of correct responses using the data shown on the previous page. (i.e., calculate the correlation and write the answer in first box). Show all your work and interpret your answer completely (write a complete interpretation in second box). (10 pts)

3. For the data shown on the previous page, find the following quantities. Show your work:

a. The percentage of variance in the number of correct responses that is shared with motivation scores. Write your final answer in the box provided. (5 pts)

b. The percentage of guessing error eliminated from predictions of the number of correct

responses made with a regression line. Write your final answer in the box provided. (5 pts)

4. A college athletics instructor was interested in the effect of aging on athletic ability. He collected the set of data shown below from a randomly selected group of physical education students.

Student # Age 100 yard dash time (in seconds)

# 1 17 12

# 2 25 10

# 3 45 18

# 4 38 20

# 5 19 14

# 6 27 12

Pearson r = .77

4a. Find the equation of the regression line for predicting 100 yard dash time from a student’s age.

Show your work. Write the regression equation in the box provided. (10 pts) 4b. Predict the 100 yard dash time in seconds for a student who is 40 years old. (5 pts)

4.c Still using the data from the previous page, forecast the amount of prediction error, in seconds (standard error of the estimate = Sest), when predicting 100 yard dash time from a student’s age. Show your work. (10 pts) Bonus question (5 pts): Nursing faculty have developed two regression models designed to predict student success in their nursing program. The models use different predictors. One model has a Pearson r correlation of .58 between the predictor and the criterion. The other model has a Pearson r correlation of .81 between the predictor and the criterion. Which model will produce a more accurate prediction of student success? Explain why. THIS QUESTION DOES NOT REQURE ANY CALCULATIONS, JUST A THOROUGH WRITTEN EXPLANATION.