1) The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?

H0:		=	110
H1:			110

Question content area bottom

Part 1

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Right-tailed

test

Two-tailed

test

Left-tailed

test

Part 2

What parameter is being tested?

Population standard deviation

Population proportion

Population mean

2)Three years ago, the mean price of an existing single-family home was

$243,713.

A real estate broker believes that existing home prices in her neighborhood are

lower.

(a)	Determine the null and alternative hypotheses.
(b)	Explain what it would mean to make a Type I error.
(c)	Explain what it would mean to make a Type II error.

Question content area bottom

Part 1

(a) State the hypotheses.

H0:

p

<

>

=

$

H1:

p

<

=

>

$

(Type integers or decimals. Do not round.)

(b) Which of the following is a Type I error?

A.The broker rejects the hypothesis that the mean price is $243,713, when it is the true mean cost.

B.The broker fails to reject the hypothesis that the mean price is $243,713, when it is the true mean cost.

C. The broker rejects the hypothesis that the mean price is $243,713, when the true mean price is less than $243,713.

D. The broker fails to reject the hypothesis that the mean price is $243,713,

when the true mean price is less than $243,713.

(c) Which of the following is a Type II error?

A. The broker rejects the hypothesis that the mean price is $243,713, when it is the true mean cost.

B. The broker fails to reject the hypothesis that the mean price is $243,713, when the true mean price is less than $243,713.

C. The broker rejects the hypothesis that the mean price is $243,713, when the true mean price is less than $243,713.

D.The broker fails to reject the hypothesis that the mean price is $243,713, when it is the true mean cost.

3)According to a report, the

standard

deviationof

monthly cell phone

bills

was

$49.26

three years ago. A researcher suspects that the

standard

deviationof

monthly cell phone

bills

is

less

today.

(a)	Determine the null and alternative hypotheses.
(b)	Explain what it would mean to make a Type I error.
(c)	Explain what it would mean to make a Type II error.

Question content area bottom

Part 1

(a) State the hypotheses.

H0:

sigma

pp

mu

not equals

greater than>

less than<

equals=

$enter your response here

H1:

sigma

mu

pp

less than<

greater than>

equals=

not equals

$enter your response here

(Type integers or decimals. Do not round.)

Part 2

(b) Explain what it would mean to make a Type I error. Choose the correct answer below.

A.

The sample evidence led the researcher to believe the

standard

deviationof

the monthly cell phone

bill

is

lessthan

$49.26,

when in fact the

standard

deviationof

the

bill

is

$49.26.

B.

The sample evidence led the researcher to believe the

standard

deviationof

the monthly cell phone

bill

is

differentfrom

$49.26,

when in fact the

standard

deviationof

the

bill

is $49.26.

C.

The sample evidence did not lead the researcher to believe the

standard

deviationof

the monthly cell phone

bill

is

differentfrom

$49.26,

when in fact the

standard

deviationof

the

bill

is

differentfrom

$49.26.

D.

The sample evidence did not lead the researcher to believe the

standard

deviationof

the monthly cell phone

bill

is

lessthan

$49.26,

when in fact the

standard

deviationof

the

bill

is

lessthan

$49.26.

Part 3

(c) Explain what it would mean to make a Type II error. Choose the correct answer below.

A.

The sample evidence did not lead the researcher to believe the

standard

deviationof

the monthly cell phone

bill

is

differentfrom

$49.26,

when in fact the

standard

deviationof

the

bill

is

differentfrom

$49.26.

B.

The sample evidence did not lead the researcher to believe the

standard

deviationof

the monthly cell phone

bill

is

lessthan

$49.26,

when in fact the

standard

deviationof

the

bill

is

lessthan

$49.26.

C.

The sample evidence led the researcher to believe the

standard

deviationof

the monthly cell phone

bill

is

lessthan

$49.26,

when in fact the

standard

deviationof

the

bill

is

$49.26.

D.

The sample evidence led the researcher to believe the

standard

deviationof

the monthly cell phone bill is

lessthan

$49.26,

when in fact the

standard

deviationof

the

bill

is

lessthan

$49.26.

4)Suppose the null hypothesis is

rejected.

State the conclusion based on the results of the test.

Three years ago, the mean price of a single-family home was

$243,704.

A real estate broker believes that the mean price has

increased

since then.

Question content area bottom

Part 1

Which of the following is the correct conclusion?

A.

There

is

sufficient evidence to conclude that the mean price of a single-family home has

increased.

B.

There

isnot

sufficient evidence to conclude that the mean price of a single-family home has not changed.

C.

There

isnot

sufficient evidence to conclude that the mean price of a single-family home has

increased.

D.

There

is

sufficient evidence to conclude that the mean price of a single-family home has not changed.

5) According to a food website, the mean consumption of popcorn annually by Americans is

61

quarts. The marketing division of the food website unleashes an aggressive campaign designed to get Americans to consume even more popcorn. Complete parts (a) through (c) below.

Question content area bottom

Part 1

(a) Determine the null and alternative hypotheses that would be used to test the effectiveness of the marketing campaign.

H0:	pp sigma mu	not equals equals=	enter your response here
H1:	sigma mu pp	greater than> less than< not equals	enter your response here

(Type integers or decimals. Do not round.)

Part 2

(b) A sample of

806

Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department.

A.

There is sufficient evidence to conclude that the mean consumption of popcorn has risen.

B.

There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.

C.

There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.

D.

There is not sufficient evidence to conclude that the mean consumption of popcorn has risen.

Part 3

(c) Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is

61

quarts. Has a Type I or Type II error been made by the marketing department? If we tested this hypothesis at the

=0.1

level of significance, what is the probability of committing this error? Select the correct choice below and fill in the answer box within your choice.

(Type an integer or a decimal. Do not round.)

A.

The marketing department committed a Type II error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type II error is

enter your response here.

B.

The marketing department committed a Type I error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type I error is

enter your response here.

C.

The marketing department committed a Type I error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type I error is

enter your response here.

D.

The marketing department committed a Type II error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type II error is

enter your response here.

6)The manufacturer of a certain engine treatment claims that if you add their product to your engine, it will be protected from excessive wear. An infomercial claims that a woman drove

3

hours without oil, thanks to the engine treatment. A magazine tested engines in which they added the treatment to the motor oil, ran the engines, drained the oil, and then determined the time until the engines seized. Complete parts (a) and (b) below.

Question content area bottom

Part 1

(a) Determine the null and alternative hypotheses that the magazine will test.

H0:

pp

sigma

mu

greater than>

less than<

equals=

not equals

3

H1:

pp

sigma

mu

equals=

less than<

not equals

greater than>

3

Part 2

(b) Both engines took exactly

14

minutes to seize. What conclusion might the magazine make based on this evidence?

A.

The infomercial's claim is not true.

B.

The infomercial's claim is true.

7) Complete parts (a) through (c) below.

(a) Determine the critical value(s) for a right-tailed test of a population mean at the

=0.01

level of significance with

15

degrees of freedom.

(b) Determine the critical value(s) for a left-tailed test of a population mean at the

=0.01

level of significance based on a sample size of

n=10.

(c) Determine the critical value(s) for a two-tailed test of a population mean at the

=0.05

level of significance based on a sample size of

n=16.

LOADING...

Click here to view the t-Distribution Area in Right Tail.

Question content area bottom

Part 1

(a)

tcrit=

plus+

minus

plus or minus

enter your response here

(Round to three decimal places as needed.)

Part 2

(b)

tcrit=

plus+

plus or minus

minus

enter your response here

(Round to three decimal places as needed.)

Part 3

(c)

tcrit=

plus or minus

minus

plus+

enter your response here

(Round to three decimal places as needed.)

8)To test

H0:

=50

versus

H1:

<50,

a random sample of size

n=24

is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.

LOADING...

Click here to view the t-Distribution Area in Right Tail.

Question content area bottom

Part 1

(a) If

x=47.7

and

s=13.4,

compute the test statistic.

t0=enter your response here

(Round to three decimal places as needed.)

Part 2

(b) If the researcher decides to test this hypothesis at the

=0.1

level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.

Critical Value:

enter your response here

(Round to three decimal places. Use a comma to separate answers as needed.)

Part 3

(c) Draw a t-distribution that depicts the critical region. Choose the correct answer below.

.

Part 4

(d) Will the researcher reject the null hypothesis?

A.

No, because the test statistic does not fall in the critical region.

B.

Yes, because the test statistic does not fall in the critical region.

C.

No, because the test statistic falls in the critical region.

D.

Yes, because the test statistic falls in the critical region.

9)In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected

15

adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of

9.02

cm3.

An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and

x=8.05

cm3

and

s=0.8

cm3.

Conduct the appropriate test at the

=0.01

level of significance.

Question content area bottom

Part 1

State the null and alternative hypotheses.

H0:

not equals

less than<

greater than>

equals=

enter your response here

H1:

equals=

not equals

greater than>

less than<

enter your response here

(Type integers or decimals. Do not round.)

Part 2

Identify the t-statistic.

t0=enter your response here

(Round to two decimal places as needed.)

Part 3

Identify the P-value.

P-value=enter your response here

(Round to three decimal places as needed.)

Part 4

Make a conclusion regarding the hypothesis.

Fail to reject

Reject

the null hypothesis. There

is not

is

sufficient evidence to claim that the mean hippocampal volume is

greater than

equal to

less than

enter your response here

cm3.