The general manager of an engineering firm wants to know whether a technical artist's experience influences the quality of his or her work. A random sample of 24 artists is selected and their years of work experience and quality rating (as assessed by their supervisors) recorded. Work experience (EXPER) is measured in years and
quality rating (RATING) takes a value of 1 through 7, with 7 = excellent and 1 =
poor. The simple regression model RATING = B1 + BEXPER + e is proposed.
The least squares estimates of the model, and the standard errors of the estimates, are
RATING = 3.204 + 0.076 EXPER
(se)
(0.709) (0.044)
(a) Sketch the estimated regression function. Interpret the coefficient of EXPER.
(b) Construct a 95% confidence interval for 2, the slope of the relationship between quality rating and experience. In what are you 95% confident?
(c) Test the null hypothesis that 2 is zero against the alternative that it is not using a
two-tail test and the a = 0.05 level of significance. What do you conclude?
(d) Test the null hypothesis that B2 is zero against the one-tail alternative that it is
positive at the a = 0.05 level of significance. What do you conclude?
(e) For the test in part (c), the p-value is 0.0982. If we choose the probability of a
Type I error to be a = 0.05, do we reject the null hypothesis, or not, just based on
an inspection of the p-value? Show, in a diagram, how this p-value is computed.