Chapter 12.1, Problem 30E

(a)

To determine

To Calculate: the difference for each subject and explain the distribution of the differences with the box plot.

Answer to Problem 30E

Yes

Explanation of Solution

Given:

  

Calculation:

Finding the difference between words and colours and words in each subject

Subject	Words	colours	Difference
1	13	20	7
2	10	21	11
3	15	22	7
4	12	25	13
5	13	17	4
6	11	13	2
7	14	32	18
8	16	21	5
9	10	16	6
10	9	13	4
11	11	11	0
12	17	26	9
13	15	20	5
14	15	15	0
15	12	18	6
16	10	18	8

Sorting the data from smallest to largest

0, 0, 2, 4, 4,5, 5, 6, 6, 7, 7, 8, 9, 11, 13, 18

The minimum is 18.

The median is

  $M=Q_2=\frac{6+6}{2}=\frac{12}{2}=6$

The first quartile

  $Q_1=\frac{4+4}{2}=\frac{8}{2}=4$

The third quartile is

  $Q_3=\frac{8+9}{2}=\frac{17}{2}=8.5$

The maximum is 18.

The inter quartile range IQR is

  $IQR=Q_3-Q_1=8.5-4=4.5$

Outliers are observations

  $\begin{array}{l}{Q}_3+1.5IQR=8.5+1.5\left(4.5\right)=15.25\\ Q_1-1.5IQR=4-1.5\left(4.5\right)=-2.75\end{array}$

Graph:

  

It is observed that 18 is greater than 15.25, therefore 18 is an outlier.

The whiskers of the box plot are at the minimum and maximum value. The box starts at the first quartile, ends at the third quartile and has a vertical line at the first quartile ends at the third quartile and has a vertical line at the median. The graph is giving the evidence of a difference in the average time need to perform the two tasks, the reason is that the most of the box plot lies to the right of 0.

(b)

To determine

To Explain: the reason of not safe to utilize paired t procedures to do inference.

Answer to Problem 30E

Data set contains an outlier

Explanation of Solution

Given:

  

The three conditions paired t procedures Random, independent (10% condition), Normal/ Large sample.

Random: satisfied, the reason is that the students were assigned to the work in random order.

Independent: Satisfied, the reason is that the sample of 16 students in the AP Statistics.

Normal/ Large sample: Not satisfied, because find that there was an outlier present in the data set (see part (a)).

Although the Normal condition is not satisfied, it is inappropriate to carrying out paired t procedures.