Chapter 5.3, Problem 108E

(a)

To determine

To find: the difference in the proportion of subjects which agreed to allow in the survey in the two groups.

Answer to Problem 108E

-0.26

Explanation of Solution

Given:

	Casual	Nice
Agreed	14	27
Declined	36	23

Calculation:

First find the column totals

	Casual	Nice
Agreed	14	27
Declined	36	23
Total	50	50

The proportion of subjects that allow participating is then the count in the “Agreed” row of the table divide by the column total.

Casual: $p_1=\frac{14}{50}=\frac{7}{25}=0.28$

Nice: $P_2=\frac{27}{50}=0.54$

The difference in proportions (Casual − Nice) is then the proportion of Casual decreased by the proportion of Nice:

  $P_1-P_2=0.28-0.54=-0.26$

(b)

To determine

To find: the differences in proportions would get due only to possibility variation in this arbitrary assignment.

Answer to Problem 108E

Not statistically significant

Explanation of Solution

Given:

  

The dots in the given dot plot shows the simulated difference (Casual −Nice)

In the proportion who agreed. It is observed that 0 lies in the mid of the bulk of dots in the dot plot that shows that a difference in proportions of 0 is likely to occur.

Although 0 is likely to get, the difference not statistically significant if 0 would have been not likely to occur, then the difference would have been statistically significant.

(c)

To determine

To find: the flaw in the design of this experiment would prevent from drawing a cause-and-effect conclusion about the affect of an interviewer’s attire on non response in a survey.

Answer to Problem 108E

The treatments were not randomly assigned to the subjects.

Explanation of Solution

Two variables are confounded when their effects on a response variable could not be distinguished from each other.

In this case, it could not be concluded that there is cause- and-effect, because the treatments were not arbitrary assigned to the subjects as they wore casual clothes on one day and nice clothes on the other day.

This then means that the day on which they wore the clothes could affect the results and therefore it could not be distinguish the day from the treatments.