Deck 7: Inferences Based on a Single Sample: Estimation With Confidence Intervals

Question 1

The Central Limit Theorem guarantees an approximately normal sampling distribution for the
sample mean for large sample sizes, so no knowledge about the distribution of the population is
necessary for the corresponding interval to be valid.

Answer 1

True

Question 2

For quantitative data, the target parameter is most likely to be the mode of the data.

Answer 2

False

Question 3

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.5%, 4.2%). What is the point estimator of the mean percentage of reservations
That are canceled on the day of the flight?

A)2.85%
B)1.35%
C)2.7%
D)2.10%

Answer 3

A

Question 4

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of
The students responded that they considered themselves full-time students. Which of the
Following would represent the target parameter of interest?

Question 5

Which statement best describes a parameter?

A)A parameter is a level of confidence associated with an interval about a sample mean or proportion.
B)A parameter is an unbiased estimate of a statistic found by experimentation or polling.
C)A parameter is a sample size that guarantees the error in estimation is within acceptable limits.
D)A parameter is a numerical measure of a population that is almost always unknown and must be estimated.

Question 6

Question 7

For data with two outcomes (success or failure), the binomial proportion of successes is likely to be
the parameter of interest.

Question 8

Since the population standard deviation σ is almost always known, we use it instead of the sample
standard deviation s when finding a confidence interval.

Question 9

Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 496 of its members at random and
Monitor the working time of each of them for 1 month. At the end of the month, the total number
Of hours absent from work is recorded for each employee. Which of the following should be used
To estimate the parameter of interest for this problem?

Question 10

Question 11

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested
In estimating the average parking time of students from within the various colleges on campus.
Which of the following would represent the target parameter of interest?

Question 12

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was
($100,951, $115,349). To make more useful inferences from the data, it is desired to reduce the
Width of the confidence interval. Which of the following will result in a reduced interval width?

A)Increase the sample size and decrease the confidence level.
B)Increase the sample size and increase the confidence level.
C)Decrease the sample size and increase the confidence level.
D)Decrease the sample size and decrease the confidence level.

Question 13

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested
In estimating the average parking time of students from within the various colleges on campus. A
Survey of 338 College of Business (COBA)students yields the following descriptive information
Regarding the length of time (in minutes)it took them to find a parking spot. Note that the ʺLo
95%ʺ and ʺUp 95%ʺ refer to the endpoints of the desired confidence interval. University officials have determined that the confidence interval would be more useful if the
Interval were narrower. Which of the following changes in the confidence level would result in a
Narrower interval?

A)The university could decrease their confidence level.
B)The university could increase their confidence level.

Question 14

Question 15

Question 16

The confidence level is the confidence coefficient expressed as a percentage.

Question 17

One way of reducing the width of a confidence interval is to reduce the confidence level.

Question 18

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects
(60-year-old male non-smokers)and constructed the following 95 percent confidence interval for
The mean cost of the term life insurance: ($850.00, $1050.00). What value of alpha was used to
Create this confidence interval?

A)0.10
B)0.025
C)0.05
D)0.01

Question 19

The registrarʹs office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and
Surveys the first 200 students who park in the chosen lot on a given day. The confidence interval is

A)not meaningful because the sampling distribution of the sample mean is not normal.
B)meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures normality of the sampling distribution of the sample mean.
C)meaningful because the sample is representative of the population.
D)not meaningful because of the lack of random sampling.

Question 20

The confidence coefficient is the relative frequency with which the interval estimator encloses the
population parameter when the estimator is used repeatedly a very large number of times.

Question 21

Question 22

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested
In estimating the average parking time of students from within the various colleges on campus. A
Survey of 338 College of Business (COBA)students yields the following descriptive information
Regarding the length of time (in minutes)it took them to find a parking spot. Note that the ʺLo
95%ʺ and ʺUp 95%ʺ refer to the endpoints of the desired confidence interval. Explain what the phrase ʺ95% confidentʺ means when working with a 95% confidence interval.

A)In repeated sampling, 95% of the population means will fall within the interval created.
B)In repeated sampling, 95% of the intervals created will contain the population mean.
C)95% of the observations in the population will fall within the endpoints of the interval.
D)In repeated sampling, 95% of the sample means will fall within the interval created.

Question 23

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects
(60-year-old male non-smokers)and constructed the following 95 percent confidence interval for
The mean cost of the term life insurance: ($850.00, $1050.00). Explain what the phrase ʺ95 percent
Confidentʺ means in this situation.

A)95 percent of all retired statisticians are underinsured.
B)95 percent of all the life insurance costs will fall within the specified interval.
C)In repeated sampling, the mean of the population will fall within the specified intervals 95 percent of the time.
D)In repeated sampling, 95 percent of the intervals constructed would contain the value of the true population mean.

Question 24

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested
In estimating the average parking time of students from within the various colleges on campus. A
Survey of 338 College of Business (COBA)students yields the following descriptive information
Regarding the length of time (in minutes)it took them to find a parking spot. Note that the ʺLo
95%ʺ and ʺUp 95%ʺ refer to the endpoints of the desired confidence interval. Give a practical interpretation for the 95% confidence interval given above.

A)We are 95% confident that the average parking time of the 338 COBA students surveyed falls between 9.19 and 11.74 minutes.
B)95% of the COBA students had parking times that fell between 9.19 and 11.74 minutes.
C)We are 95% confident that the average parking time of all COBA students falls between 9.19 and 11.74 minutes.
D)95% of the COBA students had parking times of 10.466 minutes.

Question 25

Question 26

How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show
That the sample mean was $70.00 and prior sampling indicated that the population standard
Deviation was $17.50. Use this information to create a 95 percent confidence interval for the
Population mean.

Question 27

The following data represent the scores of a sample of 50 randomly chosen students on a
standardized test. a. Write a 95% confidence interval for the mean score of all students who took the test.
b. Identify the target parameter and the point estimator.

Question 28

A random sample of 250 students at a university finds that these students take a mean of 15.8 credit hours per quarter with a standard deviation of 2.3 credit hours. Estimate the mean credit
Hours taken by a student each quarter using a 90% confidence interval. Round to the nearest
Thousandth.

Question 29

Question 30

Question 31

Which information is not shown on the screen below?

A)the confidence level
B)the sample mean
C)the sample size
D)the sample standard deviation

Question 32

Question 33

Question 34

Question 35

Question 36

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was
($146,132, $156,381). Give a practical interpretation of the interval.

A)We are 90% confident that the mean salary of the sampled CEOs falls in the interval $146,132 to $156,381.
B)90% of all CEOs in the electronics industry have salaries that fall between $146,132 to $156,381.
C)We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $146,132 to $156,381.
D)90% of the sampled CEOs have salaries that fell in the interval $146,132 to $156,381.

Question 37

Question 38

What is the confidence coefficient in a 95% confidence interval for

A).025
B).475
C).95
D).05

Question 39

Question 40

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects
(60-year-old male non-smokers)and constructed the following 95 percent confidence interval for
The mean cost of the term life insurance: ($850.00, $1050.00). State the appropriate interpretation for
This confidence interval. Note that all answers begin with ʺWe are 95 percent confidence that…ʺ

A)The term life insurance cost for all 60-year-old male non-smokersʹ insurance policies falls between $850.00 and $1050.00
B)The term life insurance cost of the retired statisticianʹs insurance policy falls between $850.00 and $1050.00
C)The average term life insurance costs for all 60-year-old male non-smokers falls between $850.00 and $1050.00
D)The average term life insurance cost for sampled 65 subjects falls between $850.00 and $1050.00

Question 41

Question 42

Question 43

Question 44

You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan,
You decide to estimate the resale value of this car with a 99% confidence interval. You manage to
Obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were
Resold at an average price of $12,760 with a standard deviation of $700. Suppose that the interval is
Calculated to be ($12,264.09, $13,255.91). How could we alter the sample size and the confidence
Coefficient in order to guarantee a decrease in the width of the interval?

A)Increase the sample size and increase the confidence coefficient.
B)Keep the sample size the same but increase the confidence coefficient.
C)Increase the sample size but decrease the confidence coefficient.
D)Decrease the sample size but increase the confidence coefficient.

Question 45

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the
College spends only the interest earned by the fund. A recent survey of eight private colleges in the
United States revealed the following endowments (in millions of dollars): 88.9, 56, 249.3, 497,
124.7, 157.6, 108.9, and 222.8. What value will be used as the point estimate for the mean
Endowment of all private colleges in the United States?

A)215.029
B)8
C)188.15
D)1505.2

Question 46

Question 47

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 99% confidence interval for
The mean was calculated to be ($2,181,260, $5,836,180). Explain what the phrase ʺ99% confidentʺ
Means.

Question 48

You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan,
You decide to estimate the resale value of this car with a 90% confidence interval. You manage to
Obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were
Resold at an average price of $12,580 with a standard deviation of $700. What is the 90% confidence
Interval for the true mean resale value of a 5- year-old car of this model?

Question 49

How much money does the average professional football fan spend on food at a single football game? That question was posed to ten randomly selected football fans. The sampled results show
That the sample mean and sample standard deviation were $70.00 and $17.50, respectively. Use
This information to create a 95 percent confidence interval for the population mean.

Question 50

How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sample results provided
A sample mean and standard deviation of $19.00 and $3.25, respectively. Use this information to
Construct a 99% confidence interval for the mean.

Question 51

Question 52

Suppose you selected a random sample of n = 29 measurements from a normal
distribution. Compare the standard normal z value with the corresponding t value for a
95% confidence interval.

Question 53

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval for
The mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary
For this confidence interval to be valid?

A)The distribution of the sample means is approximately normal.
B)The sample standard deviation is less than the degrees of freedom.
C)None. The Central Limit Theorem applies.
D)The population of total compensations of CEOs in the service industry is approximately normally distributed.

Question 54

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon.
Which of the following would represent a 90% confidence interval for the average highway
Mileage of all SmartCars?

Question 55

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval for
The mean was calculated to be ($2,181,260, $5,836,180). What would happen to the confidence
Interval if the confidence level were changed to 90%?

A)There would be no change in the width of the interval.
B)The interval would get narrower.
C)It is impossible to tell until the 90% interval is constructed.
D)The interval would get wider.

Question 56

Suppose you selected a random sample of n = 7 measurements from a normal distribution.
Compare the standard normal z value with the corresponding t value for a 90%
confidence interval.

Question 57

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week)spent studying, the
Amount of time (in hours per week)spent playing video games and the GPA - for a sample of 20
Male university students. As part of the research, a 95% confidence interval for the average GPA of
All male university students was calculated to be: (2.95, 3.10). Which of the following statements is
True?

A)In construction of the confidence interval, a z-value with 20 degrees of freedom was used.
B)In construction of the confidence interval, a t-value with 19 degrees of freedom was used.
C)In construction of the confidence interval, a t-value with 20 degrees of freedom was used.
D)In construction of the confidence interval, a z-value was used.

Question 58

Question 59

Question 60

Question 61

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week)spent studying, the
Amount of time (in hours per week)spent playing video games and the GPA - for a sample of 20
Male university students. As part of the research, a 95% confidence interval for the average GPA of
All male university students was calculated to be: (2.95, 3.10). What assumption is necessary for the
Confidence interval analysis to work properly?

A)The population that we are sampling from needs to be a t-distribution with n-1 degrees of freedom.
B)The sampling distribution of the sample mean needs to be approximately normally distributed.
C)The Central Limit theorem guarantees that no assumptions about the population are necessary.
D)The population that we are sampling from needs to be approximately normally distributed.

Question 62

Question 63

The following sample of 16 measurements was selected from a population that is
approximately normally distributed. Construct a 90% confidence interval for the population mean.

Question 64

A computer package was used to generate the following printout for estimating the mean
sale price of homes in a particular neighborhood. A friend suggests that the mean sale price of homes in this neighborhood is $46,000.
Comment on your friendʹs suggestion.

Question 65

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 148 college students produced the following confidence interval for the
Proportion of college students who prefer drink A: (.344, .494). Is this a large enough sample for
This analysis to work?

Question 66

Question 67

Question 68

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. At what level of reliability is the confidence interval made?

A)10%
B)90%
C)45%
D)55%

Question 69

You are interested in purchasing a new car. One of the many points you wish to consider
is the resale value of the car after 5 years. Since you are particularly interested in a certain
foreign sedan, you decide to estimate the resale value of this car with a 95% confidence
interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the
same model. These 17 cars were resold at an average price of $12,900 with a standard
deviation of $700. Create a 95% confidence interval for the true mean resale value of a
5-year-old car of that model.

Question 70

A marketing research company is estimating the average total compensation of CEOs in
the service industry. Data were randomly collected from 18 CEOs and the 90% confidence
interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the
confidence interval.

Question 71

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 330 college students produced the following 95% confidence interval for the
Proportion of college students who prefer one of the colas: (.330, .469). What additional
Assumptions are necessary for the interval to be valid?

A)The sample was randomly selected from an approximately normal population.
B)The population proportion has an approximately normal distribution.
C)No additional assumptions are necessary.
D)The sample proportion equals the population proportion.

Question 72

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of
The students responded that they considered themselves full-time students. A computer program
Was used to generate the following 95% confidence interval for the population proportion:
(0.64814, 0.75186). The sample size that was used in this problem is considered a large sample.
What criteria should be used to determine if n is large?

Question 73

Question 74

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or
She prefers. A computer package was used to generate the printout below for the proportion of
College students who prefer American automobiles.

Question 75

The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8.
Construct a 95% confidence interval for the population mean

Question 76

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week)spent studying, the
Amount of time (in hours per week)spent playing video games and the GPA - for a sample of 20
Male university students. As part of the research, a 95% confidence interval for the average GPA of
All male university students was calculated to be: (2.95, 3.10). The researcher claimed that the
Average GPA of all male students exceeded 2.94. Using the confidence interval supplied above,
How do you respond to this claim?

A)We are 95% confident that the researcher is incorrect.
B)We are 95% confident that the researcher is correct.
C)We cannot make any statement regarding the average GPA of male university students at the 95% confidence level.
D)We are 100% confident that the researcher is incorrect.

Question 77

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. A friend suggests that the mean sale price of homes in this neighborhood is $49,000. Comment on
Your friendʹs suggestion.

A)Your friend is correct, and you are 100% certain.
B)Your friend is wrong, and you are 95% certain.
C)Your friend is correct, and you are 95% certain.
D)Based on this printout, all you can say is that the mean sale price might be $49,000.

Question 78

A marketing research company is estimating the average total compensation of CEOs in
the service industry. Data were randomly collected from 18 CEOs and the 99% confidence
interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you
believe the average total compensation of CEOs in the service industry is more than
$1,500,000?

Question 79

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has
Recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 26.5
Milligrams and standard deviation of 2.6 milligrams for a sample of n = 9 cigarettes. Construct a
90% confidence interval for the mean nicotine content of this brand of cigarette.

Question 80

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. Which of the following is a practical interpretation of the interval above?

A)We are 90% confident that the true sale price of all homes in this neighborhood fall between $40,249.40 and $52,750.60.
B)90% of the homes in this neighborhood have sale prices that fall between $40,249.40 and $52,750.60.
C)We are 90% confident that the mean sale price of all homes in this neighborhood falls between $40,249.40 and $52,750.60.
D)All are correct practical interpretations of this interval.