June 7, 2019

ANSWERS TO REVIEW QUESTIONS

1. Distinguish between sample findings and population facts. How are they similar, and how

may they differ?

A sample finding is whenever a percentage, or an average, or some other analysis value is

computed with a sample’s data. However, because of the sample error involved, the sample

2. Define generalization, and provide an example of what you might generalize if you moved to

a new city and noticed that you were driving faster than most other drivers.

Generalization is the act of estimating a population fact from a sample finding.

With the driving example, your generalization would be based on observing that other drivers

3. What is a parameter, and what is parameter estimation?

The parameter is the actual population value being estimated (an average, or a percent).The

4. Describe how a confidence interval can be used by a researcher to estimate a population

percentage.

A confidence interval is a range (lower and upper boundary) into which the researcher

Formula for a population

percentage estimation

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level of confidence)

=

p

s

6. Using the formula for a confidence interval for a percentage, indicate the role of:

Formula for a 95%

confidence interval for a

percentage

One begins the estimation process with the sample percent, p. The variability is computed by

the product of p times q, so highly variability (e.g., 50x50) increases this product, while low

7. Indicate how a researcher interprets a 95% confidence interval. Refer to the sampling

distribution in your explanation.

The interpretation is based on the normal curve or bell-shaped distribution. The standard

error is a measure of the variability in a population based on the variability found in the

sample. If you theoretically took many, many samples and plotted the sample percentage, p,

8. In the case of a standard error of the average, indicate how it is affected by the following:

a. Standard deviation

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b. Sample size

The standard error of the average is calculated by dividing the standard deviation by the

9. What is a hypothesis and what is the purpose of a hypothesis test? With a hypothesis test

what is the null hypothesis?

A hypothesis is when one makes a statement about the population parameter based on prior

knowledge, assumptions, or intuition. This statement most commonly takes the form of an

exact specification as to what the population value is. A hypothesis test is a statistical

10. How does statistical hypothesis testing differ from intuitive hypothesis testing? How are they

similar?

Intuitive hypothesistesting (as opposed to statistical hypothesis testing) is when someone

11.When performing a hypothesis test, what critical value of z is the most commonly used one,

and to what level of significance does it pertain?

12.When the person who posited a hypothesis argues against the researcher who has performed

the hypothesis test and not supported it, who should win the argument and why?

13.Using a bell-shaped curve, show the acceptance (supported) and rejection (not supported)

regions for the following levels of confidence.

For a., the acceptance level is 95% of the bell-shaped curve (centered over the apex of the

curve), while the rejection region is the 2.5% to the left and to the right of the 95%

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14. How does a directional hypothesis differ from a nondirectional one, and what are the two

critical items to take into account when testing a directional hypothesis?

A directional hypothesis is one that indicates the direction in which you believe the

population parameter falls relative to some hypothesized average or percentage. When testing

a directional (greater than or less than) hypothesis, the critical z value is adjusted downward

ANSWERS TO APPLICATION QUESTIONS

15. Here are several computation practice exercises in which you must identify which

formula should be used and to apply it. In each case, after you perform the necessary

calculations, write your answers in the blank column.

a. Determine confidence intervals for each of the following:

Mean of 150, stdev. of 30, n of 200, level of 95%—

use average confidence interval

Percent of 67%, n of 300, level of 99%—use percentage formula

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0.767

300

58.267

Mean of 5.4, stdev. of 0.5, n of 250, level of 99%—use average formula

Percent of 25.8%, n of 500, level of 99%—use percentage formula

b. Test the following hypothesis and interpret your findings.

Hypothesis: mean=7.5, mean of 8.5, s.d. of 1.2, n of 670, level of 95%

The hypothesis is not supported.

Hypothesis: percent=86%, p of 95%, n of 1,000, level of 99%

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4 8.532.5

08.4.5

58.24.5

x

x

z

The hypothesis is not supported.

Hypothesis: mean greater than 125, mean of 135, s.d. of 15, n of 500, level of 95%

The hypothesis is supported.

Hypothesis: percent less than 33%, p of 31, n of 120,level of 99%

The hypothesis is not supported.

16. The manager of Washington State Environmental Services Division wants a survey that will

tell her how many households in the city of Seattle will voluntarily identify environmentally

hazardous household materials like old cans of paint, unused pesticides, and other such

materials than cannot be recycled, but should be disposed of and then transport all of their

environmental hazardous items to a central disposal center located in the downtown area

and open only on Sunday mornings. A random survey of 500 households determines that

20% of households would do so, and that each participating household expects to dispose of

about five items per year with a standard deviation of two items. What is the value of

parameter estimation in this instance?

Parameter estimation will be useful in estimating the percent of households in the population

who will take part in the recycling program, and it can be used to estimate the number of

aluminum cans that each household will recycle monthly, on the average.

To estimate the percent of households, apply the confidence interval formula for a percent.

The 95% level of confidence is used below.

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9.14

67.

10

500

15

z

48.

2.4

2

120

)69)(31(

3331

z

To estimate the number of cans, apply the confidence interval formula for a mean. Note,

Combining the two estimates with the population of the city will yield an estimate of the total

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6.3 20

500

n

pxq

s

s

x 1.96 x

x

17. It is reported in the newspaper that a survey sponsored by Forbes magazine with 200

Fortune 500 company top executives has found that 75% believe that the United States trails

Japan and Germany in automobile engineering. What percent of all Fortune 500 company

top executives believe that the United States trails Japan and Germany?

18.Alamo Rent-A-Car executives believe that Alamo accounts for about 50% of all Cadillacs

that are rented. To test this belief, a researcher randomly identifies twenty major airports

with on-site rental car lots. Observers are sent to each location and instructed to record the

number of rental company Cadillacs observed in a four--hour period. About 500 are

observed, and 30% are observed being returned to Alamo Rent-A-Car. What are the

implications of this finding for the Alamo executives' belief?

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% - %

00

x

n

pxq

s

p

175

2

75

A computed z of -9.76 does not support the hypothesis.

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-p

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=z

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p