The general manager of an engineering firm wants to know if a technical artist's experience influences the quality of their 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 = ?1 +?2EXPER+e is proposed. The least squares estimates of the model, and the standard errors of the estimates are RATING = 3.204 + 0.076EXPER (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 ? = 0.05 level of significance. What do you conclude?

(d) Test the null hypothesis that ?2 is zero against the one-tail alternative that it is positive at the ? = 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 ? = 0.05, do we reject the null hypothesis or not, just based on an inspection of the p-value? Show, in a diagram how the p-value is computed.