Question

The Apprenticecontestants’ performance ratings. Referto the Significance(April 2015) study of contestants’ performanceson the United Kingdom’s version of the TVshow, The Apprentice, Exercise 2.9 (p. 73). Recall thatthe performance of each of 159 contestants was rated ona 20-point scale. Contestants were also divided into twogroups: those who played for a job and those who playedfor a businesspartnership. These data (simulated, based onstatistics reportedin the article) are saved in the accompanyingfile. Descriptive statistics for each of the two groupsof contestants are displayed in the accompanying Minitabprintout.

a. Determine whether the performance ratings of contestantswho played for a job are approximately normallydistributed.

b. Determine whether the performance ratings of contestantswho played for a business partnership are approximatelynormally distributed.

Descriptive Statistics: Rating

Variable Rating	Price	N	Mean	St.Dev	Minimum	Q 1	median	Q3	Maximum	IQ R
	Job	99	7.879	4.224	1	4	9	11	20	7
	Partner	60	8.883	4.809	1	5	8	12	20	7

Short answer

a. The data is not normally distributed

b. The data is notapproximately normally distributed.

Step-by-step solution

Given Information

For the contestants who played for a job, the St.dev is 4.224 and the IQR is 7.

For the contestants who played for a business partnership, the St.dev is 4.809 and the IQR is 7.

Looking for normality

a.

$$\begin{gathered} \frac{IQR}{s}=\frac{7}{4.224} \\ =1.65719697 \\ ﲔ1.7 \end{gathered}$$

Here the value of IQR/s is not equal to 1.3. So, the performance ratings of contestants who played for a job are not normally distributed.

Looking for approximate normality

b.

$$\begin{gathered} \frac{IQR}{s}=\frac{7}{4.809} \\ =1.455604076 \\ ﲔ1.5 \end{gathered}$$

Here, the value of IQR/s is not equal to 1.3, so the performance ratings of contestants who played for a business partnership are not approximately normally distributed