Deck 12: Inference About a Population

Question 1

Marketing segmentation separates consumers of a product into different groups in such a way that members of each group are ____________________ and there are differences between ____________________.

Answer 1

similar; groups

Question 2

NARRBEGIN: Healthy foods
Healthy Foods
In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet consciousness as the segmentation variable. Four segments are developed and coded as follows:
To distinguish between groups, surveys are conducted. On the basis of a questionnaire, people are categorized as belonging to one of these groups. A recent survey asked a random sample of 1,500 Spanish adults (20 and over) to complete the survey. Out of the 1,500 people surveyed, 360 indicated that they are concerned about eating healthy foods. The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over.NARREND
{Healthy Foods Narrative} What is the objective of this problem?

Answer 2

The problem objective is to describe the population of Spanish adults in terms of their health and diet consciousness.

Question 3

In estimating the population mean $\mu$ when the population size N is small, the confidence interval estimator of $\mu$ is $\bar { x } \pm t _ { \omega / 2 } \cdot \frac { s } { \sqrt { n } } \sqrt { \frac { N - n } { N - 1 } }$ .

Answer 3

True

Question 4

In estimating the total of a population of size N, where N is very large compared to the sample size, the confidence interval estimator of the total is $N \left[ \bar { x } \pm t _ { \alpha / 2 } \cdot s / \sqrt { n } \right]$ .

Question 5

To estimate ____________________ when the population size N is small, the confidence interval estimator is $\bar { x } \pm t _ { \omega / 2 } \cdot \frac { s } { \sqrt { n } } \sqrt { \frac { N - n } { N - 1 } }$ .

Question 6

When a population is small relative to the sample size, we must incorporate the ____________________ factor in the calculation of the standard error of estimate of the mean.

Question 7

Which of the following statements is false?

A)Because there is one single way to segment a market, managers must consider several variable or characteristics that could be used to identify segments.
B)Surveys of customers are used to gather data about various aspects of the market.
C)Statistical techniques are applied to the survey data to define the market segments.
D)Market segmentation separates consumers of a product into different groups in such a way that members of each group are similar to each other and there are differences between groups.

Question 8

Target marketing focuses on satisfying the demands of all segments of the entire market.

Question 9

Generally speaking, mass marketing has given way to target marketing, which focuses on satisfying the demands of a particular segment of the entire market.

Question 10

A population is defined to be small if it is ____________________ than ____________________ times the size of the sample.

Question 11

Mass marketing refers to the mass production and marketing by a company of all products the company produces for a single segment of the entire market.

Question 12

Which of the following statements is correct regarding mass marketing?

A)It refers to the mass production and marketing by a company of a single product for the entire market.
B)It is especially effective for commodity goods such as gasoline, which are very difficult to differentiate from the competition, except through price and convenience of availability.
C)Generally speaking, mass marketing has given way to target marketing, which focuses on satisfying the demands of a particular segment of the entire market.
D)All of these choices are true.

Question 13

If the lower and upper confidence limits of the population proportion p, using a sample of size 1500, are 0.184 and 0.238, respectively, then the lower and upper confidence limits of the total number of successes in the population, given that the population size is 750,000, are respectively:

A)276 and 357
B)137,724 and 178,143
C)138,000 and 178,500
D)138,276 and 179,857

Question 14

Market segmentation separates consumers of a product into different groups in such a way that members of each group are similar to each other and there are differences between groups.

Question 15

In market segmentation, if education is the segmentation variable of interest, then possible segments of the market include: some high school, high school graduates, some college, college or university graduates.

Question 16

Mass marketing is especially effective for ____________________ goods such as gasoline, which are difficult to differentiate from the competition except through price and availability.

Question 17

If the lower and upper confidence limits of the population mean $\mu$ , using a sample of size 100, are 225 and 280, respectively, then the lower and upper confidence limits of the total of a population of size 3000 are respectively

A)652,500 and 812,000
B)675,000 and 840,000
C)697,500 and 868,000
D)652,862 and 812,452

Question 18

When is the finite population correction used?

A)When the population is more than or equal to 20 times the sample size.
B)When the population is less than or equal to 20 times the population size.
C)When the population is equal to 20 times the population size.
D)Whenever the sample size is small, no matter what the population size is.

Question 19

Mass Marketing refers to the mass production and marketing by a company of a single product for the entire market.

Question 20

____________________ refers to the mass production and marketing by a company of a single product for the entire market.

Question 21

NARRBEGIN: Healthy foods
Healthy Foods
In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet consciousness as the segmentation variable. Four segments are developed and coded as follows:
To distinguish between groups, surveys are conducted. On the basis of a questionnaire, people are categorized as belonging to one of these groups. A recent survey asked a random sample of 1,500 Spanish adults (20 and over) to complete the survey. Out of the 1,500 people surveyed, 360 indicated that they are concerned about eating healthy foods. The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over.NARREND
{Healthy Foods Narrative} Interpret the confidence interval of p.

Question 22

NARRBEGIN: Healthy foods
Healthy Foods
In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet consciousness as the segmentation variable. Four segments are developed and coded as follows:
To distinguish between groups, surveys are conducted. On the basis of a questionnaire, people are categorized as belonging to one of these groups. A recent survey asked a random sample of 1,500 Spanish adults (20 and over) to complete the survey. Out of the 1,500 people surveyed, 360 indicated that they are concerned about eating healthy foods. The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over.NARREND
{Healthy Foods Narrative} Estimate with 95% confidence the proportion p of Spanish adults who classify themselves as concerned about eating healthy.

Question 23

The sampling distribution of $\hat { p }$ is approximately normal if the sample size is more than 30.

Question 24

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion $\tilde { p }$ , we:

A)take another sample and estimate.
B)take two more samples and find the average of their.
C)let= 0.50.
D)let= 0.95.

Question 25

NARRBEGIN: Healthy foods
Healthy Foods
In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet consciousness as the segmentation variable. Four segments are developed and coded as follows:
To distinguish between groups, surveys are conducted. On the basis of a questionnaire, people are categorized as belonging to one of these groups. A recent survey asked a random sample of 1,500 Spanish adults (20 and over) to complete the survey. Out of the 1,500 people surveyed, 360 indicated that they are concerned about eating healthy foods. The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over.NARREND
{Healthy Foods Narrative} What is the point estimate of the proportion p of Spanish adults who classify themselves as concerned about eating healthy?

Question 26

NARRBEGIN: Healthy foods
Healthy Foods
In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet consciousness as the segmentation variable. Four segments are developed and coded as follows:
To distinguish between groups, surveys are conducted. On the basis of a questionnaire, people are categorized as belonging to one of these groups. A recent survey asked a random sample of 1,500 Spanish adults (20 and over) to complete the survey. Out of the 1,500 people surveyed, 360 indicated that they are concerned about eating healthy foods. The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over.NARREND
{Healthy Foods Narrative} Estimate with 95% confidence thee number of Spanish adults who classify themselves as concerned about eating healthy.

Question 27

The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

Question 28

In testing a hypothesis about a population proportion p, the z test statistic measures how close the computed sample proportion $\tilde { p }$ has come to the hypothesized population parameter.

Question 29

The lower limit of the 90% confidence interval for the population proportion p, given that n = 400 and $\hat { p }$ = 0.10, is 0.0247.

Question 30

NARRBEGIN: Tractor Dealership
Tractor Dealership
An accountant was performing an audit for a tractor dealership. An auditor wants to examine the monetary error made by the purchasing order department in the month of July. He decided to randomly sample 100 of the 925 purchase orders for the month of July, and found the amount of error in each one. The statistics for this sample were: = $6.0 and s = $17.012.NARREND
{Tractor Dealership Narrative} Estimate with 95% confidence the total amount of monetary error for the month of July.

Question 31

If we have some idea about the value of sample proportion $\tilde{ p }$ , we use that value in determining the sample size needed to estimate the population proportion p.

Question 32

The use of the standard normal distribution for constructing confidence interval estimate for the population proportion p requires:

A)nand n(1 -) both greater than 5.
B)np and n(1 - p) both greater than 5.
C)n(1 +) and n(1-) both greater than 5.
D)sample size greater than 5.

Question 33

A professor of statistics refutes the claim that the proportion of Republican voters in Michigan is at most 44%. To test the claim, the hypotheses: H₀: p = 0.44, H₁: p $\neq$ 0.44, should be used.

Question 34

NARRBEGIN: Tractor Dealership
Tractor Dealership
An accountant was performing an audit for a tractor dealership. An auditor wants to examine the monetary error made by the purchasing order department in the month of July. He decided to randomly sample 100 of the 925 purchase orders for the month of July, and found the amount of error in each one. The statistics for this sample were: = $6.0 and s = $17.012.NARREND
{Tractor Dealership Narrative} Why should the finite population correction factor (FPCF) be used for this problem? Explain.

Question 35

In determining the sample size needed to estimate the population proportion p, we let the sample proportion $\hat { p }$ = 1 if we have no knowledge of even the approximate values of $\hat { p }$ .

Question 36

NARRBEGIN: Healthy foods
Healthy Foods
In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet consciousness as the segmentation variable. Four segments are developed and coded as follows:
To distinguish between groups, surveys are conducted. On the basis of a questionnaire, people are categorized as belonging to one of these groups. A recent survey asked a random sample of 1,500 Spanish adults (20 and over) to complete the survey. Out of the 1,500 people surveyed, 360 indicated that they are concerned about eating healthy foods. The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over.NARREND
{Healthy Foods Narrative} What is the parameter we wish to estimate? Explain.

Question 37

NARRBEGIN: Tractor Dealership
Tractor Dealership
An accountant was performing an audit for a tractor dealership. An auditor wants to examine the monetary error made by the purchasing order department in the month of July. He decided to randomly sample 100 of the 925 purchase orders for the month of July, and found the amount of error in each one. The statistics for this sample were: = $6.0 and s = $17.012.NARREND
{Tractor Dealership Narrative} Estimate with 95% confidence the average amount of error per purchase order for the entire month of July.

Question 38

Under what condition(s) does the test statistic for p have an approximate normal distribution?

A)When np > 5.
B)When np and np(1 -p) are both > 5.
C)When n > 30.
D)When np and n(1 - p) are both > 5.

Question 39

After calculating the sample size needed to estimate a population proportion to within 0.04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led to a sample size of 800, the sample size will now have to be:

A)800
B)3,200
C)6,400
D)12,800

Question 40

Assuming that all necessary conditions are met, what needs to be changed in the formula $\tilde { p } \pm t _ { a } \sqrt { \tilde { p } ( 1 - \tilde { p } ) / n }$ so that we can use it to construct a (1 - $\alpha$ ) confidence interval estimate for the population proportion p?

A)should be replaced by p.
B)t _$\alpha$ should be replaced by z _$\alpha$ .
C)t _$\alpha$ should be replaced by t _{$\alpha$ / 2}.
D)t _$\alpha$ should be replaced by z _{$\alpha$ / 2}.

Question 41

NARRBEGIN: Physicians
Physicians
A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year.NARREND

-{Physicians Narrative} Construct a 99% confidence interval estimate of the population proportion of physicians who make at least $400,000 a year, and explain how to use it to test the hypotheses.

Question 42

The formula is used to find the ____________________ to estimate a population proportion.

Question 43

NARRBEGIN: Physicians
Physicians
A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year.NARREND

-{Physicians Narrative} Compute the p-value and explain how to use it to test the hypotheses.

Question 44

The test statistic for p is approximately normal when ____________________ and ____________________ are both greater than 5.

Question 45

The test statistic for p is approximately normal when np and n(1 - p) are both ____________________.

Question 46

When a population is small, it is necessary to include the ____________________ factor in our hypothesis tests and confidence interval estimators for p.

Question 47

NARRBEGIN: Physicians
Physicians
A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year.NARREND

-{Physicians Narrative} Can we conclude at the 1% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24?

Question 48

The formula is used to find the sample size needed to estimate a population proportion. In this formula, B represents the ____________________ on the error of estimation.

Question 49

NARRBEGIN: Socialist Voters
Socialist Party Voters
A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that. In a test of hypothesis, H₀: p = 0.05 vs. H₁: p < 0.05, his random sample of size 1,000 registered voters revealed that the number of Socialists was 40.NARREND

-{Socialist Voters Narrative} Compute the p-value and explain how to use it to test the hypotheses.

Question 50

When determining the sample size needed for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be:

A)the smaller the sample size required.
B)the larger the sample size required.
C)the sample size is not affected.
D)the effect cannot be determined from the information given.

Question 51

To test to see if the majority of the population exhibits a certain characteristic of interest, the alternative hypothesis of the test is H₁: p ____________________.

Question 52

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors' results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:

A)-1.67
B)-2.33
C)-1.86
D)-0.14

Question 53

NARRBEGIN: Socialist Voters
Socialist Party Voters
A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that. In a test of hypothesis, H₀: p = 0.05 vs. H₁: p < 0.05, his random sample of size 1,000 registered voters revealed that the number of Socialists was 40.NARREND

-{Socialist Voters Narrative} Test the hypotheses at the 5% significance level.

Question 54

Estimating or testing for p is used in situations when the data are ____________________.

Question 55

From a sample of 400 items, 14 are found to be defective. The point estimate of the population proportion defective will be:

A)0.035
B)0.05
C)14
D)28.57

Question 56

To produce a confidence interval estimator for the total, we multiply the lower and upper confidence limits of the interval estimator of p by ____________________.

Question 57

Which of the following would be an appropriate null hypothesis?

A)The population proportion is equal to 0.60.
B)The sample proportion is equal to 0.60.
C)The population proportion is not equal to 0.60.
D)All of these choices are true.

Question 58

NARRBEGIN: Socialist Voters
Socialist Party Voters
A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that. In a test of hypothesis, H₀: p = 0.05 vs. H₁: p < 0.05, his random sample of size 1,000 registered voters revealed that the number of Socialists was 40.NARREND

-{Socialist Voters Narrative} Construct a 95% confidence interval estimate of the population proportion and explain how to use it to test the hypotheses.

Question 59

Which of the following would be an appropriate alternative hypothesis?

A)The population proportion is less than 0.65.
B)The sample proportion is less than 0.65.
C)The population proportion is equal to 0.65.
D)The sample proportion is equal to 0.65.

Question 60

The width of a confidence interval estimate for a proportion will be:

A)narrower for 90% confidence than for 95% confidence.
B)wider for a sample size of 100 than for a sample size of 50.
C)narrower for 99% confidence than for 95% confidence.
D)narrower when the sample proportion if 0.50 than when the sample proportion is 0.20.

Question 61

NARRBEGIN: Pilots' Union Contract
Pilots' Union Contract
A union composed of several thousand pilots is preparing to vote on a new contract. A random sample of 500 pilots yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes.NARREND
{Pilots' Union Contract Narrative} Can we infer at the 5% significance level that the new contract will receive more than 60% yes votes?

Question 62

A left-tailed area in the chi-squared distribution equals 0.95. For 6 degrees of freedom the critical value equals 12.592.

Question 63

NARRBEGIN: Pilots' Union Contract
Pilots' Union Contract
A union composed of several thousand pilots is preparing to vote on a new contract. A random sample of 500 pilots yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes.NARREND
{Pilots' Union Contract Narrative} State the appropriate null and alternative hypotheses.

Question 64

NARRBEGIN: New Mousetrap
New Mousetrap
After a financial analysis, the general manager of a large company decided that if more than 8% of potential buyers of a new mousetrap purchase that product, the company would show a profit. In a preliminary survey of 500 potential buyers, 56 people say that they will buy the mousetrap.NARREND
{New Mousetrap Narrative} State the appropriate null and alternative hypotheses.

Question 65

The test statistic used to test hypotheses about the population variance is given by $\chi$ ² = (n -1)s² / $\sigma$ ², which is chi-squared distributed with n -1 degrees of freedom when the population is normally distributed with variance equal to $\sigma$ ².

Question 66

The chi-squared distribution can be used in constructing confidence intervals and carrying out hypothesis tests regarding the value of a population variance.

Question 67

NARRBEGIN: Sinus Drug
Sinus Drug
A company claims that 10% of the users of a certain sinus drug experience drowsiness. In clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness
NARREND
{Sinus Drug Narrative} Construct a 95% confidence interval estimate of the population proportion of the users of this allergy drug who experience drowsiness.

Question 68

The statistic s² is an unbiased and consistent estimator of $\sigma$ ².

Question 69

Two uses for the population variance are to measure risk and consistency.

Question 70

The area to the right of a certain critical value on a chi-squared distribution is 0.025. For 5 degrees of freedom, the critical value is 11.143.

Question 71

As a manufacturer of guitars, a major corporation wants to estimate the proportion of guitar players who are right-handed. How many golfers must be surveyed if they want to be within 0.02, with a 95% confidence?
a.Assume that there is no prior information that could be used as an estimate of.
b.Assume that the manufacturer has an estimate offound from a previous study, which suggests that 75% of guitar players are right-handed.

Question 72

NARRBEGIN: Sinus Drug
Sinus Drug
A company claims that 10% of the users of a certain sinus drug experience drowsiness. In clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness
NARREND
{Sinus Drug Narrative} Compute the p-value of the test.

Question 73

A condition of using the chi-squared test statistic for testing the variance is that the population random variable have a normal distribution.

Question 74

Which of the following is not an example illustrating the use of variance?

A)As a measure of risk.
B)As a judge of consistency.
C)To search for and reduce variability in a process.
D)All of these choices are true.

Question 75

NARRBEGIN: Sinus Drug
Sinus Drug
A company claims that 10% of the users of a certain sinus drug experience drowsiness. In clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness
NARREND

-{Sinus Drug Narrative} Explain how to use this confidence interval to test the hypotheses.

Question 76

A random sample is drawn from a normal distribution with mean $\mu$ and variance $\sigma$ ². The random variable (n - 1)S² / $\sigma$ ² has a chi-squared probability distribution with n degrees of freedom.

Question 77

NARRBEGIN: Pilots' Union Contract
Pilots' Union Contract
A union composed of several thousand pilots is preparing to vote on a new contract. A random sample of 500 pilots yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes.NARREND
{Pilots' Union Contract Narrative} Compute the p-value for the test.

Question 78

NARRBEGIN: Sinus Drug
Sinus Drug
A company claims that 10% of the users of a certain sinus drug experience drowsiness. In clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness
NARREND

-{Sinus Drug Narrative} We want to test their claim and find out whether the actual percentage is not 10%. State the appropriate null and hypotheses.

Question 79

NARRBEGIN: New Mousetrap
New Mousetrap
After a financial analysis, the general manager of a large company decided that if more than 8% of potential buyers of a new mousetrap purchase that product, the company would show a profit. In a preliminary survey of 500 potential buyers, 56 people say that they will buy the mousetrap.NARREND
{New Mousetrap Narrative} Is there sufficient evidence at the 5% significance level that the mousetrap will produce a profit?

Question 80

NARRBEGIN: Sinus Drug
Sinus Drug
A company claims that 10% of the users of a certain sinus drug experience drowsiness. In clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness
NARREND

-{Sinus Drug Narrative} Is there enough evidence at the 5% significance level to infer that the competitor is correct?