Refer to the Significance (April 2015) study of contestants' performance on the popular TV show The Apprentice, Exercise 2.9 (p. 49). Recall that each of 159 contestants was rated (on a 20-point scale) based on their performance. The accompanying Minitab printout gives the mean and standard deviation of the contestant ratings, categorized by highest degree obtained (no degree, first degree, or postgraduate degree) and prize (job or partnership with Lord Sugar).

a. Give a practical interpretation of the mean rating for contestants with a first (bachelor's) degree who competed for a job with Lord Sugar.
b. Find an interval that captures about 95% of the ratings for contestants with a first (bachelor's) degree who competed for a job with Lord Sugar.
c. An analysis of the data led the researchers to conclude that "when the reward for winning . . . was a job, more academically qualified contestants tended to perform less well; however, this pattern is reversed when the prize changed to a business partnership." Do you agree? Explain.

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Descriptive Statistics: Rating Results for Prize = Job Variable Degree N Rating Mean SEDev Minimum Maximun 1.000 17.000 20.0০০ 17.00 Tirat 54 7.796 4.231 None 35 7.457 4.30e 10 9.80 1.000 2.00 Dost 4.54 Results for Prize - Partner Variable Degree N Mean sEDav Minimum Maximum 20.000 20.0০ 12.00 Rating 33 8.212 4.775 4.83 3.33 Tirst None Post 1.000 3.00 2.00 21 10.62 6.50