A large sample of students was surveyed at a particular university. Among other things, they were asked to report their age and how much money they had earned in the previous year, in thousands of dollars.
a. Use software to access the student survey data and produce a scatterplot of earnings versus age. Which of these best expresses the circumstances for this particular data set?
1. The responses are non-normal and the sample size is small.
2. The responses are non-normal and the sample size is large.
3. The responses are normal and the sample size is small.
4. The responses are normal and the sample size is large.
b. Find the correlation r and the P-value, and choose the best word in both cases to summarize the results: There is (1) weak/borderline/strong evidence of a (2) weak/moderate/strong relationship in the population.
c. Produce the regression equation and complete this rough summary of the relationship: Take a student's age and subtract ______ to find an estimate for how many thousands of dollars we predict to be earned.
d. According to the regression output, predictions of earnings based on age tend to be off by about how many dollars?
e. In general, which is narrower: a confidence interval for the mean response or a prediction interval for an individual response?
f. Considering that the students' mean age was about 20 years, which would be narrower: interval estimates when age equals 20 or when age equals 30?
g. Use software to produce a confidence interval for mean earnings and prediction interval for individual earnings when age equals 20, and also for when age equals 30. Indicate which is the narrowest of the four intervals and which is the widest.
h. A value of 3.5 thousand dollars is not plausible for which one of the following: mean earnings of all 20-year-old students in the population, mean earnings of all 30-year-old students in the population, earnings of an individual 20-year-old in the population, or earnings of an individual 30-year-old student in the population?