Question

Recycle and Review Exercises 29-31 refer to the following setting. Does the color in which words are printed affect your ability to read them? Do the words themselves affect your ability to name the color in which they are printed? Mr. Starnes designed a study to investigate these questions using the 16 students in his AP Statistics class as subjects. Each student performed the following two tasks in random order while a partner timed his or her performance: (1) Read $32$words aloud as quickly as possible, and (2) say the color in which each of $32$words is printed as quickly as possible. Try both tasks for yourself using the word list given.

Color words (10.3) Now let's analyze the data,

a Calculate the difference (Colors-Words) (Colors - Words) for each subject and surmmarize thedistribution of differences with a boxplot. does the graph provide evidence of a difference in the average time required to perform the two tests? Explain your answer.

b. Explain why it is not safe to use paired & procedures to do inference about the mean difference in time in complete the Two tasks.

Short answer

a. Yes, the graph provide evidence of a difference in the average time required to perform the two tests

b.It is not safe to use paired & procedures to do inference about the mean difference in time in complete the Two tasks because of data set contains an outlier.

Step-by-step solution

Part (a) Step 1: Given Information

Given table is

We have to calculate the difference (Colors-Words) (Colors - Words) for each subject and surmmarize thedistribution of differences with a boxplot. and also determine does the graph provide evidence of a difference in the average time required to perform the two tests .

Part (a) Step 2: Explanation 

The difference (Colors-Words) (Colors - Words) for each subject

The Medain is$6$

1st quartile is$4$

3rd quartile is$8.5$

IQR$4.5$

outliers are observations

$Q_3+1.5IQR=8.5+1.5(4.5)=15.25$

$Q_1-1.5IQR=4-1.5(4.5)=-2.75$

Graph:

Due to the fact that $18$is larger than $15.25$it is considered an anomaly.

The box plot's whiskers are at the minimum and highest values. The box has a vertical line at the first quartile, ends at the third quartile, and starts at the first quartile, ends at the third quartile, and starts at the median. The fact that the majority of the box plot sits to the right of $0$indicates that there is a difference in the average time required to complete the two tasks.

 Part (b) Step 1: Given Information 

The given table is

We have to explain why it is not safe to use paired & procedures to do inference about the mean difference in time in complete the Two tasks .

Part (b) Step 2: Explanation 

The students were assigned to the job in a random order, so they were satisfied. independent: Satisfied, according to the sample size of 16 students in AP Statistics.

Sample size: normal/large: Not satisfied, because an outlier was discovered in the data set (see part (a)).

Even if the Normal condition is not met, performing paired t operations is not recommended.