Question

# Researchers wondered if there was a difference between males and females in regard to some common...

Researchers wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and​ females, the following​ question: "Are you annoyed by people who repeatedly check their mobile phones while having an​ in-person conversation?" Among the

517517

males​ surveyed,

168168

responded​ "Yes"; among the

545545

females​ surveyed,

204204

responded​ "Yes." Does the evidence suggest a higher proportion of females are annoyed by this​ behavior? Complete parts​ (a) through​ (g) below.

(a) Determine the sample proportion for each sample.

The proportions of the females and males who took the survey who are annoyed by the

behavior in questionbehavior in question

are

nothing

and

nothing​,

respectively.

​(Round to four decimal places as​ needed.)

​(b) Explain why this study can be analyzed using the methods for conducting a hypothesis test regarding two independent proportions. Select all that apply.

A.

The samples are dependent.

B.

The data come from a population that is normally distributed.

C.

n 1 ModifyingAbove p with caret 1 left parenthesis 1 minus ModifyingAbove p with caret 1 right parenthesis greater than or equals 10n1p11−p1≥10

and n 2 ModifyingAbove p with caret 2 left parenthesis 1 minus ModifyingAbove p with caret 2 right parenthesis greater than or equals 10n2p21−p2≥10

D.

The sample size is more than​ 5% of the population size for each sample.

E.

The samples are independent.

F.

The sample size is less than​ 5% of the population size for each sample.

​(c) What are the null and alternative​ hypotheses? Let

p 1p1

represent the population proportion of females who are annoyed by the

behavior in questionbehavior in question

and

p 2p2

represent the population proportion of males who are annoyed by the

behavior in questionbehavior in question.

Upper H 0H0​:

p 1p1

less than<

equals=

not equals≠

greater than>

p 2p2

Upper H 1H1​:

p 1p1

not equals≠

less than<

equals=

greater than>

p 2p2​(d) Describe the sampling distribution of

ModifyingAbove p with caret Subscript femalepfemaleminus−ModifyingAbove p with caret Subscript malepmale.

Draw a normal model with the area representing the​ P-value shaded for this hypothesis test.The sampling distribution is approximately normal with mean

nothing

and standard deviation

nothing.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

Draw a normal model with the area representing the​ P-value shaded for this hypothesis test. Choose the correct graph​ below, where the horizontal axis represents

ModifyingAbove p with caret Subscript femalepfemaleminus−ModifyingAbove p with caret Subscript malepmale.

A.0

font size decreased by 2 0.0490.049

A normal curve is over a horizontal axis and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 0.049. The area under the curve and to the left of the vertical line segment is shaded.

B.0

font size decreased by 2 0.0490.049

A normal curve is over a horizontal axis and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 0.049. The area under the curve and to the right of the vertical line segment is shaded.

C.0

font size decreased by 2 negative 0.049−0.049

A normal curve is over a horizontal axis and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at negative 0.049. The area under the curve and to the left of the vertical line segment is shaded.

D.0

font size decreased by 2 negative 0.049−0.049

A normal curve is over a horizontal axis and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at negative 0.049. The area under the curve and to the right of the vertical line segment is shaded.

​(e) Determine the​ P-value based on the model from part​ (d).

First find the test statistic for this hypothesis test.

nothing

​(Round to two decimal places as​ needed.)

Determine the​ P-value for this hypothesis test.

nothing

​(Round to three decimal places as​ needed.)

​(f) Interpret the​ P-value.

If the population proportions are

not equal,

equal,

one would expect a sample difference proportion

greater than the absolute value ofgreater than the absolute value of

greater thangreater than

smaller than the absolute value ofsmaller than the absolute value of

smaller thansmaller than

the one observed in about

nothing

out of 1000 repetitions of this experiment.

​(Round to the nearest integer as​ needed.)

​(g) Based on the​ P-value, what does the sample evidence​ suggest? That​ is, what is the conclusion of the hypothesis​ test? Assume an

alphaαequals=0.010.01

level of significance.

A.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence at the

alphaαequals=0.010.01

level of significance to suggest a higher proportion of females are annoyed by the

behavior in questionbehavior in question.

B.

Do not rejectDo not reject

Upper H 0H0.

There

isis

sufficient evidence at the

alphaαequals=0.010.01

level of significance to suggest a higher proportion of females are annoyed by the

behavior in questionbehavior in question.

C.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence at the

alphaαequals=0.010.01

level of significance to suggest a higher proportion of females are annoyed by the

behavior in questionbehavior in question.

D.

Do not rejectDo not reject

Upper H 0H0.

There

is notis not

sufficient evidence at the

alphaαequals=0.010.01

level of significance to suggest a higher proportion of females are annoyed by the

behavior in questionbehavior in question.

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