Question

Researchers created two test sheets, each sheet showing 20 photos of the faces of dog‑owner pairs. The two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet the dogs were matched with their owners, while on the second sheet the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog‑owner pairs that resemble each other, Sheet 11 or Sheet 22 ," and were simply told the aim of the research was a "survey on dog‑owner relationships." In the first experiment, the original sheets were shown to subjects; in the second experiment, just the mouth region of the owners was blacked out in all the pictures on both sheets; while in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and in each experiment, the number of subjects who selected the sheet with the dogs and their owners correctly matched was recorded. Experimenters were interested in whether blacking out portions of the faced reduced the ability of subjects to correctly match dogs and owners. The results are displayed.

Experiment	Number of Subjects	Number Correctly Matched
Experiment 11	61	49
Experiment 22 (mouth blacked out)	51	37
Experiment 33 (eyes blacked out)	60	30

(a) Is there evidence that blacking out the mouth reduces a subject's ability to choose the sheet which correctly matches the dogs and their owners?

Use the four‑step process to answer the question.

STATE: Which choice best describes the statement of this experiment/study.

1)We want to know if blacking out the mouth region reduces a subject's ability to correctly match the dog‑owner pairs.

2)This is an experiment, since it includes two independent samples.

3)This is an experiment, since the samples are taken randomly.

4)This is an observational study, since the variable of interest is measured but there is no attempt to influence the responses.

5)This is an observational study, since it applies to female Hispanic drivers alone.

PLAN: To examine whether the null hypothesis is true we should test the hypotheses:

?0:?1≠?2 versus ??:?1=?2

?0:?1=?2 versus ??:?1<?2

?0:?1=?2versus ??:?1>?2

?0:?1=?2 versus ??:?1≠?2

SOLVE: Assume the samples can be thought of as an SRS. We can conduct a hypothesiss test since there are more than five successes (correctly identified the pairs) and more than five failures in each sample. Calculate ?̂ 1,?̂ 2, and ?̂. (Enter your answers rounded to four decimal places.)

?̂ 1=

?̂ 2=

?̂ =

Compute the z test statistic. (Enter your answer rounded to four decimal places.)

?=

Using the software of your choice, calculate the one–sided P‑value for the null hypothesis. (Enter your answer rounded to three decimal places.)

?=

CONCLUDE: Which conclusion is correct?

1)There is not enough evidence to conclude that blacking out the mouth region reduces a subject's ability to correctly match dog‑owner pairs.

2)There is enough evidence to conclude that blacking out the mouth region reduces a subject's ability to correctly match dog‑owner pairs.

(b) Is there evidence that blacking out the eyes reduces a subject's ability to choose the sheet which correctly matches the dogs and their owners?

STATE: We want to know if blacking out the mouth region reduces a subject's ability to correctly match the dog‑owner pairs.

PLAN: To examine whether the null hypothesis is true we should test the hypotheses:

?0:?1=?2 versus ??:?1<?2

?0:?1=?2 versus ??:?1≠?2

?0:?1≠?2 versus ??:?1=?2

?0:?1=?2versus ??:?1>?2

SOLVE: Assume the samples can be thought of as an simple random sample. We can conduct a hypothesis test since there are more than five successes (correctly identified the pairs) and more than five failures in each sample. Calculate ?̂ 1,?̂ 2, and ?̂ . (Enter your answers for ?̂ 1 and ?̂ rounded to four decimal places, and your answer for ?̂ 2 rounded to one decimal place.)

?̂ 1=

?̂ 2=

?̂ =

Compute the z test statistic. (Enter your answer rounded to one decimal place.)

?=

Using the software of your choice, find the P‑value for the null hypothesis.

0.05<?

0.005<?<0.05

0.0005<?<0.005

?<0.0005

CONCLUDE: Which conclusion is correct?

1)There is strong evidence that blacking out the eye region reduces one's ability to match dog‑owner pairs.

2)There is weak evidence that blacking out the eye region reduces one's ability to match dog‑owner pairs.

(c) Contrast your conclusions in part (a) and (b) in the context of the problem. Select the best choice.

1)The evidence in (a) and (b) are too close to make a conclusion.

2)The conclusions in parts (a) and (b) imply the mouth region plays a larger role in matching dogs than the eye region does.

3)The conclusions in parts (a) and (b) imply the eye region plays a larger role in matching dogs than the mouth region does.

Answer 1

(a)

STATE : Correct choice that best describes the statement of this experiment/study :

We want to know if blacking out the mouth region reduces a subject's ability to correctly match the dog‑owner pairs.

PLAN: To examine whether the null hypothesis is true we should test the hypotheses:

SOLVE:

Z test statistic is :

P -value = P = 0.166

CONCLUDE :

There is not enough evidence to conclude that blacking out the mouth region reduces a subject's ability to correctly match dog‑owner pairs.

(b)

STATE : Correct choice that best describes the statement of this experiment/study :

We want to know if blacking out the eyes region reduces a subject's ability to correctly match the dog‑owner pairs.

PLAN: To examine whether the null hypothesis is true we should test the hypotheses:

SOLVE:

Z test statistic is :

P -value = P = 0.0002

Hence,

CONCLUDE :

There is strong evidence that blacking out the eye region reduces one's ability to match dog‑owner pairs.

Now,

Best choice :

The conclusions in parts (a) and (b) imply the eye region plays a larger role in matching dogs than the mouth region does.