Question

A professor at a local university designed an experiment to see if someone could identify the color of a candy based on taste alone. Students were blindfolded and then given a​ red-colored or​ yellow-colored candy to chew.​ (Half the students were assigned to receive the red candy and half to receive the yellow candy. The students could not see what color candy they were​ given.) After​ chewing, the students were asked to guess the color of the candy based on the flavor. Of the

122122

students who participated in the​ study,

7878

correctly identified the color of the candy. The results are shown in the accompanying technology printout. Complete parts a through c below.

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Click the icon to view the technology printout.

a. If there is no relationship between color and candy​ flavor, what proportion of the population of students would correctly identify the​ color?

The proportion would be

0.50.5.

​(Type an integer or a​ decimal.)

b. Specify the null and alternative hypotheses for testing whether color and flavor are related. Choose the correct hypotheses below.

A.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p greater than 0.50H0: p=0.50 vs. Ha: p>0.50

B.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p less than 0.50H0: p=0.50 vs. Ha: p<0.50

C.

Upper H 0 : p not equals 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p≠0.50 vs. Ha: p=0.50

Your answer is not correct.

D.

Upper H 0 : p less than 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p<0.50 vs. Ha: p=0.50

E.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p not equals 0.50H0: p=0.50 vs. Ha: p≠0.50

This is the correct answer.

F.

Upper H 0 : p greater than 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p>0.50 vs. Ha: p=0.50

c.

Carry out the test and give the appropriate conclusion at

alphaαequals=0.010.01.

Use the​ p-value of the​ test, shown on the accompanying technology​ printout, to make your decision.

The​ p-value is

0.0020.002.

​(Type an integer or a​ decimal.)

Make the appropriate conclusion using

alphaαequals=0.010.01.

A.

RejectReject

the null​ hypothesis, because the​ p-value is

not less thannot less than

alphaα.

There is

insufficientinsufficient

evidence to conclude that color and flavor are related.

B.

Do not rejectDo not reject

the null​ hypothesis, because the​ p-value is not

not less thannot less than

alpha

Answer 1

Result:

122 students who participated in the​ study, 78 correctly identified the color of the candy. The results are shown in the accompanying technology printout. Complete parts a through c below.

a. If there is no relationship between color and candy​ flavor, what proportion of the population of students would correctly identify the​ color?

The proportion would be 0.5 .

b. Specify the null and alternative hypotheses for testing whether color and flavor are related. Choose the correct hypotheses below.

E.

H0: p=0.50 vs. Ha: p≠0.50

c.

Carry out the test and give the appropriate conclusion at alphaαequals=0.01.

Use the​ p-value of the​ test, shown on the accompanying technology​ printout, to make your decision.

The​ p-value is 0.002.

Make the appropriate conclusion using alphaαequals=0.01.

Reject the null​ hypothesis, because the​ p-value is less than alpha α.

There is sufficient evidence to conclude that color and flavor are related.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.5
Level of Significance	0.01
Number of Items of Interest	78
Sample Size	122
Intermediate Calculations
Sample Proportion	0.639344262
Standard Error	0.0453
Z Test Statistic	3.0782
Two-Tail Test
Lower Critical Value	-2.5758
Upper Critical Value	2.5758
p-Value	0.0021
Reject the null hypothesis