Question

The Apprenticecontestants’ performance ratings.Refer to the Significance(April 2015) study of contestants’ performance on the popular TV show The Apprentice, Exercise 2.9 (p. 73). 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).

Descriptive Statistics: Ratings
Results for Prize = Job
Variable	Degree	N	Mean	StDev	Minimum	Maximum
Rating	First	54	7.796	4.231	1.000	17
	None	35	7.457	4.388	1.000	20
	Post	10	9.80	4.54	2.000	17
Results for Prize = Partnership
Variable	Degree	N	Mean	StDev	Minimum	Maximum
Rating	First	33	8.212	4.775	1.000	20.00
	None	21	10.62	4.83	3.000	20.00
	Post	6	6.50	3.33	2.000	12.00

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.

Short answer

(a) Mean = 7.796

(b) Interval = -0.666 to 16.258

Step-by-step solution

Interpreting the mean rating for contestants with a first (bachelor’s) degree who competed for a job with Lord Sugar

The mean rating is 7.796. Therefore, it means that, on average, contestants with a first (bachelor’s) degree got a 7.796 rating on their performance on the show.

Finding the interval that captures about 95% of the ratings for contestants with a first (bachelor’s) degree who competed for a job with Lord Sugar

Mean for first (bachelor’s) degree contestants for job = 7.796

Standard deviation for first (bachelor’s) degree contestants for job = 4.231

We need to find the interval that captures 95% of the ratings, and according to the empirical rule, 2 standard deviations from the mean captures 95% of the ratings.

To find the actual interval, we will use $\overline{x}\pm 2s$

$$\begin{gathered} Lowerrange=\overline{x}-2s \\ =7.796-2(4.231) \\ =7.796-8.462 \\ =-0.666 \\ Upperrange=\overline{x}+2s \\ ==7.796+2(4.231) \\ =7.796+8.462 \\ =16.258 \end{gathered}$$

Therefore, the interval that captures 95% of the ratings is -0.666 to 16.258.

 Step 3: Inferring the data

No, I disagree because when the reward changes from Job to Partnership, contestants with first degree and no degree perform better. Whereas, it is observed that contestants with postgraduate degrees perform better when the reward is a job compared to the reward as a partnership.