Researchers created two test sheets, each sheet showing 20 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 1 1 or Sheet 2 2 ," 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 1 1 61 61 49 49 Experiment 2 2 (mouth blacked out) 51 51 37 37 Experiment 3 3 (eyes blacked out) 60 60 30 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. This is an observational study, since the variable of interest is measured but there is no attempt to influence the responses. This is an observational study, since it applies to female Hispanic drivers alone. We want to know if blacking out the mouth region reduces a subject's ability to correctly match the dog‑owner pairs. This is an experiment, since the samples are taken randomly. This is an experiment, since it includes two independent samples. PLAN: To examine whether the null hypothesis is true we should test the hypotheses: ? 0 : ? 1 = ? 2 H0:p1=p2 versus ? ? : ? 1 ≠ ? 2 Ha:p1≠p2 ? 0 : ? 1 = ? 2 H0:p1=p2 versus ? ? : ? 1 > ? 2 Ha:p1>p2 ? 0 : ? 1 ≠ ? 2 H0:p1≠p2 versus ? ? : ? 1 = ? 2 Ha:p1=p2 ? 0 : ? 1 = ? 2 H0:p1=p2 versus ? ? : ? 1 < ? 2 Ha:p1
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Researchers created two test sheets, each sheet showing
20
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
1
1
or Sheet
2
2
," 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
1
1
61
61
49
49
Experiment
2
2
(mouth blacked out)
51
51
37
37
Experiment
3
3
(eyes blacked out)
60
60
30
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.
This is an observational study, since the variable of interest is measured but there is no attempt to influence the responses.
This is an observational study, since it applies to female Hispanic drivers alone.
We want to know if blacking out the mouth region reduces a subject's ability to correctly match the dog‑owner pairs.
This is an experiment, since the samples are taken randomly.
This is an experiment, since it includes two independent samples.
PLAN: To examine whether the null hypothesis is true we should test the hypotheses:
?
0
:
?
1
=
?
2
H0:p1=p2
versus
?
?
:
?
1
≠
?
2
Ha:p1≠p2
?
0
:
?
1
=
?
2
H0:p1=p2
versus
?
?
:
?
1
>
?
2
Ha:p1>p2
?
0
:
?
1
≠
?
2
H0:p1≠p2
versus
?
?
:
?
1
=
?
2
Ha:p1=p2
?
0
:
?
1
=
?
2
H0:p1=p2
versus
?
?
:
?
1
<
?
2
Ha:p1<p2
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
?
̂
p^1,p^2, and p^
. (Enter your answers rounded to four decimal places.)
?
̂
1
=
p^1=
?
̂
2
=
p^2=
?
̂
=
p^=
Compute the
?
z
test statistic. (Enter your answer rounded to four decimal places.)
?=
z=
Using the software of your choice, calculate the one–sided
?
P
‑value for the null hypothesis. (Enter your answer rounded to three decimal places.)
?=
P=
CONCLUDE: Which conclusion is correct?
There is not enough evidence to conclude that blacking out the mouth region reduces a subject's ability to correctly match dog‑owner pairs.
There is enough evidence to conclude that blacking out the mouth region reduces a subject's ability to correctly match dog‑owner pairs.
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