Question

1. Marcus wants to determine how age and weight are related to exercise preference in his town. He selects a simple random sample of 75 overweight individuals from the 25- to 35-year age group and records their age, weight, and exercise preference (sports, Pilates/yoga, dancing, none). He also selects an independent simple random sample of 50 normal-weight individuals from the 40- to 50-year age group and records the same information. Which is the most important observation about Marcus's plan?

a. He should have selected the two age groups randomly instead of choosing them specifically.

b. He will be unable to tell whether a difference in exercise preference is related to a difference in age or to a difference in weight.

c. The plan is well conceived and should serve the intended purpose.

d. His samples are too small.

e. He should have used equal sample sizes.

2. An analyst wants to determine the relationship between speed, in miles per hour, and the time, in hours, it takes to drive 5 miles. Twenty trials are completed and the correlation coefficient between speed and time is determined to be -0.276. Therefore, slower speed was related to greater time. How is the correlation affected if the units for time are changed from hours to minutes?

a. The correlation and time measurement would change proportionally to one another.

b. The correlation would increase because changing the units for time would result in an increase in time values.

c. The correlation would stay the same because the change in units for time would have no effect on it.

d. It is impossible to determine the amount of change experienced by the correlation.

e. The correlation would decrease because only the units for one of the variables changed.

3. Monthly private school tuition based on the average number of weeks in attendance is predicted using the least-square regression line, ŷ = 265.9 + 93.4x, where ŷ represents the predicted monthly expense and x represents the average number of weeks in attendance. A child attends private school an average of 3.5 weeks and has a monthly cost of $595. What is the residual for the child?

a. −2.2

b. 2.2

c. 3.52

d. −3.52

e. 90.7

Answer 1

1.

The two groups are overweight young age group and normal weight 40- to 50-year age group. For any significant difference, we cannot conclude that the difference is due to differences in weights or age among the groups.

b. He will be unable to tell whether a difference in exercise preference is related to a difference in age or to a difference in weight.

2.

The correlation between variables does not changes with changes in the units of the variables.

c. The correlation would stay the same because the change in units for time would have no effect on it.

3.

The estimated regression line is,

ŷ = 265.9 + 93.4x

For x = 3.5, predicted y is,

ŷ = 265.9 + 93.4 * 3.5 = 592.8

Residual = Actual - Predicted = 595 - 592.8 =  2.2

b. 2.2