# Stat Test questions and answers Sample Assignment

A company produces a single product on three production lines that use different equipment. The production manager is considering changing the layouts of the lines and would like to know what effects different layouts would have on production output. Suppose that the manager measured the average output for each line over three randomly selected weeks using each of the three layouts under consideration. The output (in hundreds of units produced) was measured for each line for each of the four weeks for each layout being evaluated. The results are shown in the accompanying table. Complete parts a through c below.

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- Based on the sample data, can the production manager conclude that there is an interaction effect between the type of layout and the production line? Conduct the appropriate test at the

0.050.05

level of significance.

Identify the hypotheses for the interaction between production line and layout. Choose the correct answer below.

A.

Upper H 0H0:

Production line and layout do not interact,

Upper H Subscript Upper AHA:

Production line and layout do interact

Your answer is correct.

B.

Upper H 0H0:

mu Subscript Upper A Baseline equals mu Subscript Upper BμA=μB,

Upper H Subscript Upper AHA:

mu Subscript Upper A Baseline not equals mu Subscript Upper BμA≠μB

C.

Upper H 0H0:

mu Subscript Upper A Baseline not equals mu Subscript Upper BμA≠μB,

Upper H Subscript Upper AHA:

mu Subscript Upper A Baseline equals mu Subscript Upper BμA=μB

D.

Upper H 0H0:

Production line and layout do interact,

Upper H Subscript Upper AHA:

Production line and layout do not interact

Find the p-value for the interaction between production line and layout.

p-valueequals=0.7110.711

(Round to three decimal places as needed.)

Draw the appropriate conclusion for the interaction between production line and layout. Choose the correct answer below.

A.

RejectReject

the null hypothesis. There is

insufficientinsufficient

evidence to conclude that the means differ.

B.

RejectReject

the null hypothesis. There is

sufficientsufficient

evidence to conclude that production line and layout interact.

C.

Do not rejectDo not reject

the null hypothesis. There is

insufficientinsufficient

evidence to conclude that the means differ.

D.

Do not rejectDo not reject

the null hypothesis. There is

insufficientinsufficient

evidence to conclude that production line and layout interact.

This is the correct answer.

- At the

0.050.05

level of significance, can the production manager conclude that there is a difference in mean output across the three production lines?

Identify the hypotheses to test for production line. Choose the correct answer below.

A.

Upper H 0H0:

mu Subscript Upper A 1 Baseline not equals mu Subscript Upper A 2 Baseline not equals mu Subscript Upper A 3μA1≠μA2≠μA3,

Upper H Subscript Upper AHA:

mu Subscript Upper A 1 Baseline equals mu Subscript Upper A 2 Baseline equals mu Subscript Upper A 3μA1=μA2=μA3

B.

Upper H 0H0:

mu Subscript Upper A Baseline equals mu Subscript Upper BμA=μB,

Upper H Subscript Upper AHA:

mu Subscript Upper A Baseline not equals mu Subscript Upper BμA≠μB

C.

Upper H 0H0:

mu Subscript Upper A 1 Baseline equals mu Subscript Upper A 2 Baseline equals mu Subscript Upper A 3μA1=μA2=μA3,

Upper H Subscript Upper AHA:

mu Subscript Upper A 1 Baseline greater than mu Subscript Upper A 2 Baseline greater than mu Subscript Upper A 3μA1>μA2>μA3

D.

Upper H 0H0:

mu Subscript Upper A 1 Baseline equals mu Subscript Upper A 2 Baseline equals mu Subscript Upper A 3μA1=μA2=μA3,

Upper H Subscript Upper AHA:

Not all production line means are equal

This is the correct answer.

Find the p-value for production lines.

p-valueequals=0.0370.037

(Round to three decimal places as needed.)

Draw the appropriate conclusion for production lines. Choose the correct answer below.

A.

Do not rejectDo not reject

the null hypothesis. There is

sufficientsufficient

evidence to conclude that the means differ.

B.

RejectReject

the null hypothesis. There is

sufficientsufficient

evidence to conclude that not all production line means are equal.

This is the correct answer.

C.

Do not rejectDo not reject

the null hypothesis. There is

insufficientinsufficient

evidence to conclude that not all production line means are equal.

D.

It is inappropriate to draw a conclusion from this test because production line and layout interact.

c At the

0.050.05

level of significance, can the production manager conclude that there is a difference in mean output due to the type of layout used?

Identify the hypotheses to test for layout. Choose the correct answer below.

A.

Upper H 0H0:

mu Subscript Upper B 1 Baseline equals mu Subscript Upper B 2 Baseline equals mu Subscript Upper B 3μB1=μB2=μB3,

Upper H Subscript Upper AHA:

Not all layout means are equal

This is the correct answer.

B.

Upper H 0H0:

mu Subscript Upper A Baseline equals mu Subscript Upper BμA=μB,

Upper H Subscript Upper AHA:

mu Subscript Upper A Baseline not equals mu Subscript Upper BμA≠μB

C.

Upper H 0H0:

mu Subscript Upper B 1 Baseline equals mu Subscript Upper B 2μB1=μB2,

Upper H Subscript Upper AHA:

Not all layout means are equal

D.

Upper H 0H0:

mu Subscript Upper B 1 Baseline not equals mu Subscript Upper B 2 Baseline not equals mu Subscript Upper B 3μB1≠μB2≠μB3,

Upper H Subscript Upper AHA:

mu Subscript Upper B 1 Baseline equals mu Subscript Upper B 2 Baseline equals mu Subscript Upper B 3μB1=μB2=μB3

Find the p-value for layout.

p-valueequals=0.0000.000

(Round to three decimal places as needed.)

Draw the appropriate conclusion for layout. Choose the correct answer below.

A.

Do not rejectDo not reject

the null hypothesis. There is

sufficientsufficient

evidence to conclude that the means differ.

B.

Do not rejectDo not reject

the null hypothesis. There is

insufficientinsufficient

evidence to conclude that not all layout means are equal.

C.

RejectReject

the null hypothesis. There is

sufficientsufficient

evidence to conclude that not all layout means are equal.

This is the correct answer.

D.

It is inappropriate to draw a conclusion from this test because production line and layout interact.

A company produces treadmills for use in exercise clubs and recreation centers. The treadmill motors are purchased from an outside vendor. Currently, the company is considering which motor to include in its new treadmill series. Three potential suppliers have been identified. The company has decided to make its decision based on how long a motor operates at a high level of speed and incline before it fails. A random sample of 10 motors of each type is selected, and each motor is tested to determine how many minutes (rounded to the nearest minute) it operates before it needs to be repaired. Use the accompanying sample information for each motor to complete parts and b.

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- At the

alphaαequals=0.050.05

level of significance, is there a difference in the average times before failure for the three different suppliers' motors?

Identify the hypotheses for the test. Choose the correct answer below.

A.

H0:

muμ1not equals≠muμ2not equals≠muμ3

HA:

At least two of the population means are equal

B.

H0:

muμ1equals=muμ2equals=muμ3

HA:

At least two of the population means are different

This is the correct answer.

C.

H0:

muμ1not equals≠muμ2not equals≠muμ3

HA:

All of the population means are equal

D.

H0:

muμ1equals=muμ2equals=muμ3

HA:

All of the population means are different

Find the test statistic F.

Fequals=7.017.01

(Round to two decimal places as needed.)

Now find the p-value.

p-valueequals=0.0030.003

(Round to three decimal places as needed.)

Reject

the null hypothesis. There is

sufficient

evidence at the

alphaαequals=0.050.05

level of significance that

at least two

of the population means are

different.

- Is it possible for the company to decide on a single motor supplier based on the analysis of the sample results? Support your answer by conducting the appropriate post test analysis.

It

is

possible for the company to decide on a single motor supplier based on the analysis of the sample results. A post test analysis such as the Tukey-Kramer procedure

is

appropriate because the null hypothesis

was

rejected.

If the post-test analysis is appropriate, identify the differences between the motors using the Tukey-Kramer procedure. Select all that apply.

A.

Them mean for Motor B is significantly different than the mean for Motor C.

B.

The mean for Motor A is significantly different than the mean for Motor C.

This is the correct answer.

C.

The mean for Motor A is significantly different than the mean for Motor B.

D.

There are no differences between the means of any of the motors.

E.

The Tukey-Kramer procedure is not appropriate.

A theater is interested in estimating the variance in sales at the snack bar on Friday nights. Suppose a random sample of

1414

Friday evenings is selected and the snack bar sales for each evening are recorded. The results of the sample in dollars are shown in the accompanying table. Use the random sample of sales to develop a

9595%

confidence interval estimate of the variance of Friday night snack bar sales.

A company manufactures and ships four different products. Breakage cost is expensive, and the company would like to select a mode of delivery (rail, plane, or truck) that reduces the amount of breakage. The company decided to examine the dollar amount of breakage incurred by the three modes of transportation. In order to control for fragility differences due to type of product, the company randomly assigns each product to each carrier and monitors the dollar breakage that occurs over the Assignment of 100 shipments. The dollar breakage per shipment (to the nearest dollar) is shown in the accompanying table. Complete parts a and b.

A plywood company makes plywood for use in furniture production. In the first major step in the plywood process, a lathe rotates the logs through a knife that peels the log into layers. Ideally, when a log is reduced to a 4-inch core diameter, the lathe releases the core. Before peeling, the logs are conditioned in a heated water-filled vat to warm them. Two factors are believed to affect the core diameter: the vat temperature and the time the logs spend in the vat prior to peeling. The lathe supervisor recently conducted a test during which logs were peeled at each combination of temperature and time. The data are the core diameters in inches. Complete parts a through d.

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a. nbspa. |
Determine if there is interaction between the temperatures and the soaking times. Use the p-value approach and a significance level of 0.0250.025. |

Find the hypotheses. Choose the correct answer below.

A.

Upper H 0H0:

Temp and Time do interact to affect the core diameter

Upper H Subscript Upper AHA:

Temp and Time do not interact to affect the core diameter

B.

Upper H 0H0:

Temp and Time do not interact to affect the core diameter

Upper H Subscript Upper AHA:

Temp and Time do interact to affect the core diameter

This is the correct answer.

C.

Upper H 0H0:

Temp and Time do interact to affect the core diameter

Upper H Subscript Upper AHA:

Not all Temp and Time means are equal

Find the test statistic.

Fequals=2.1272.127

(Round to three decimal places as needed.)

Find the p-value.

p-valueequals=0.0900.090

(Round to three decimal places as needed.)

Choose the correct conclusion below.

A.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence that the temperature and soaking time do interact to affect the core diameter.

B.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence that not all temperature and soaking time means are equal.

C.

Do not rejectDo not reject

Upper H 0H0.

There is

sufficientsufficient

evidence that the temperature and soaking time do interact to affect the core diameter.

D.

Do not rejectDo not reject

Upper H 0H0.

There is

insufficientinsufficient

evidence that the temperature and soaking time do interact to affect the core diameter.

This is the correct answer.

b. nbspb. |
Given your findings in part a, determine if there is a difference in the average core diameter for the temperatures. Use a test-statistic approach with a significance level of 0.0250.025. |

Let the formula be factor A and plant be factor B. Find the hypotheses. Choose the correct answer below.

A.

Upper H 0H0:

At least two temperatures have different averages of core diameter

Upper H Subscript Upper AHA:

mu Subscript Upper A 1 Baseline equals mu Subscript Upper A 2 Baseline equals mu Subscript Upper A 3 Baseline equals mu Subscript Upper A 4μA1=μA2=μA3=μA4

B.

Upper H 0H0:

mu Subscript Upper A 1 Baseline equals mu Subscript Upper A 2 Baseline equals mu Subscript Upper A 3 Baseline equals mu Subscript Upper A 4μA1=μA2=μA3=μA4

Upper H Subscript Upper AHA:

At least two temperatures have different averages of core diameter

This is the correct answer.

C.

Upper H 0H0:

mu Subscript Upper A 1 Baseline equals mu Subscript Upper A 2 Baseline equals mu Subscript Upper A 3 Baseline equals mu Subscript Upper A 4μA1=μA2=μA3=μA4

Upper H Subscript Upper AHA:

mu Subscript Upper A 1 Baseline not equals mu Subscript Upper A 2 Baseline not equals mu Subscript Upper A 3 Baseline not equals mu Subscript Upper A 4μA1≠μA2≠μA3≠μA4

Find the test statistic.

Fequals=16.16016.160

(Round to three decimal places as needed.)

Find the critical value.

Upper F Subscript alphaFαequals=4.0774.077

(Round to three decimal places as needed.)

Choose the correct conclusion below.

A.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence that

mu Subscript Upper A 1 Baseline not equals mu Subscript Upper A 2 Baseline not equals mu Subscript Upper A 3 Baseline not equals mu Subscript Upper A 4μA1≠μA2≠μA3≠μA4.

B.

Do not rejectDo not reject

Upper H 0H0.

There is

sufficientsufficient

evidence to indicate that at least two temperatures have different averages of core diameter.

C.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to indicate that at least two temperatures have different averages of core diameter.

This is the correct answer.

D.

Do not rejectDo not reject

Upper H 0H0.

There is

insufficientinsufficient

evidence that

mu Subscript Upper A 1 Baseline not equals mu Subscript Upper A 2 Baseline not equals mu Subscript Upper A 3 Baseline not equals mu Subscript Upper A 4μA1≠μA2≠μA3≠μA4.

- nbspc. Repeat

part b for the soaking times.

Find the hypotheses. Choose the correct answer below.

A.

Upper H 0H0:

mu Subscript Upper B 1 Baseline equals mu Subscript Upper B 2 Baseline equals mu Subscript Upper B 3 Baseline equals mu Subscript Upper B 4μB1=μB2=μB3=μB4

Upper H Subscript Upper AHA:

At least two soaking times have different averages of core diameter

This is the correct answer.

B.

Upper H 0H0:

mu Subscript Upper B 1 Baseline not equals mu Subscript Upper B 2 Baseline not equals mu Subscript Upper B 3 Baseline not equals mu Subscript Upper B 4μB1≠μB2≠μB3≠μB4

Upper H Subscript Upper AHA:

mu Subscript Upper B 1 Baseline equals mu Subscript Upper B 2 Baseline equals mu Subscript Upper B 3 Baseline equals mu Subscript Upper B 4μB1=μB2=μB3=μB4

C.

Upper H 0H0:

At least two soaking times have different averages of core diameter

Upper H Subscript Upper AHA:

mu Subscript Upper B 1 Baseline equals mu Subscript Upper B 2 Baseline equals mu Subscript Upper B 3 Baseline equals mu Subscript Upper B 4μB1=μB2=μB3=μB4

Find the test statistic.

Fequals=2.5602.560

(Round to three decimal places as needed.)

Find the p-value.

p-valueequals=0.0910.091

(Round to three decimal places as needed.)

Choose the correct conclusion below.

A.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence that

mu Subscript Upper B 1 Baseline equals mu Subscript Upper B 2 Baseline equals mu Subscript Upper B 3 Baseline equals mu Subscript Upper B 4μB1=μB2=μB3=μB4.

B.

Do not rejectDo not reject

Upper H 0H0.

There is

insufficientinsufficient

evidence that at least two soaking times have different averages of core diameter.

This is the correct answer.

C.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence that at least two soaking times have different averages of core diameter..

D.

Do not rejectDo not reject

Upper H 0H0.

There is

sufficientsufficient

evidence that

A random sample of

1616

values was selected from a population, and the sample standard deviation was computed to be

- 120120.

Based on this sample result, compute a

9090%

confidence interval estimate for the true population standard deviation.

92.9692.96less than or equals≤sigmaσless than or equals≤172.48

Given the accompanying null hypothesis, alternative hypothesis, and sample information, complete parts a and b below.

The production control manager of a company is interested in determining whether there is a difference in standard deviation of product diameter for parts made at plant A versus those made at plant B. Plant A is highly automated and thought to provide better quality control. Thus, the parts produced in plant B should be more variable than those made at plant A. A random sample of

1414

parts was selected from those produced last week at plant A. The standard deviation for these parts was

0.170.17

inch. A sample of

1313

parts was selected from those made in plant B. The sample standard deviation for these parts was

0.220.22

inch.

A stage company solicits donations to help fund its operations. It obtained the help of a marketing research company whose representatives proposed two different solicitation brochures. They are interested in determining whether there is a difference in the standard deviation of dollars returned between the two brochures. To test this, a random sample of

1616

people was selected to receive brochure A and another random sample of

1616

people was selected to receive brochure B. The donation amounts are shown in the accompanying table. Based on these sample data, what should the stage company conclude about the two brochures with respect to their variability? Test using a significance level of

0.050.05.

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Suppose as part of your job you are responsible for installing emergency lighting in a series of state office buildings. Bids have been received from four manufacturers of battery-operated emergency lights. The costs are about equal, so the decision will be based on the length of time the lights last before failing. A sample of four lights from each manufacturer has been tested with the following values (time in hours) recorded for each manufacturer. Assume that the data are approximately normal. Complete parts a and b.

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a. nbspa. |
Using a significance level of 0.010.01, what conclusion should you reach about the four manufacturers' battery-operated emergency lights? Explain. |

Identify the hypotheses for the test. Choose the correct answer below.

The human resources director of a large company recently asked her staff to conduct a study of the airline miles traveled by executives of the company during the most recent calendar year. The analyst assigned to the project randomly sampled

1616

male executives and

1616

female executives. Of particular interest to the HR director is whether males have greater variability in miles flown than females. The statistics available below were computed from the samples. Based on these data, what should the HR director conclude if an alpha level equal to

0.050.05

is used?

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A manager is interested in determining if the population standard deviation has dropped below

- 144144.

Based on a sample of

nequals=1717

items selected randomly from the population, conduct the appropriate hypothesis test at a

0.050.05

significance level. The sample standard deviation is

133133.

A rope manufacturer tested the breaking strength of several types of ropes over a 10-day period. The results of the study are shown in the accompanying table. Complete parts a through c.

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Most auto batteries are made by just three

manufacturerslong dash—A,

B, and C. Use the sample data available below to determine if who makes the auto batteries affects the average length of life of the battery. The data represent the length of life (months) for batteries of the same specifications for each of the three manufacturers. Complete parts a and b below.

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Statistics from a specific government bureau indicate the average wage for construction workers is about

$21.3121.31

an hour. Its survey suggests that construction wages can vary widely. The highest-paying region's wages are approximately

3232%

larger, and the lowest-paying region's wages are about

3030%

lower than the national average. A sample of

2222

construction workers in a third region yielded an average wage of

$12.2712.27

and a standard deviation of

$1.411.41.

Complete parts a and b below.

Find the appropriate critical F-value for each of the following using the F-distribution table.