Deck 9: Estimation From Sample Data

Question 1

To use the t distribution for a small sample size when deriving a confidence interval requires that the population be normally distributed.

Answer 1

True

Question 2

A 0.95 confidence coefficient is equivalent to a 5% confidence level.

Answer 2

False

Question 3

A confidence interval is an estimate for which there is a specified degree of certainty that the population parameter will be in the interval.

Answer 3

True

Question 4

The Student's t distribution has a mean of zero and the shape is determined by the number of degrees of freedom.

Question 5

With other factors unchanged,a lower confidence level will require a wider confidence interval.

Question 6

If a sample has 16 observations and a 95% confidence estimate for $\mu$ is needed,the appropriate t-score is 1.746.

Question 7

The more certain we wish to be that the interval estimate contains the population parameter,the wider the interval will have to be.

Question 8

The sample statistic s is an unbiased estimator of the population parameter $\text { ? }$
when (n - 1)is used as a divisor when we calculate the standard deviation of the sample.

Question 9

The t distribution is used to calculate a confidence interval when the population is normally distributed and the population standard deviation is known.

Question 10

In determining the necessary sample size in making an interval estimate for a population mean,it is necessary to first make an estimate of the population standard deviation.

Question 11

A 95% confidence interval means that there is a 95% probability that the interval will include the true population mean.

Question 12

A confidence interval will allow us to say with complete certainty that our sample result will actually include the population mean.

Question 13

If the population mean $\mu$ is unknown,one can use sample data as the basis from which to make probability statements about the true (but unknown)value of $\mu$ .

Question 14

If the population mean $\mu$ and population standard deviation $\text {? }$
are both known and a sample size that is greater than 30,one can invoke the central limit theorem and make probability statements about the means of samples taken from the population.

Question 15

Whenever sample data are used for estimating a population mean or proportion,sampling error will not be present,since the observed sample statistic ( $\bar { x }$ or p)will not differ from the actual value of the population parameter ( $\mu$ or $\pi$ ).

Question 16

If a sample has 16 observations from a normal population and a 90% confidence estimate for $\mu$ is needed,the appropriate t-score is 2.12.

Question 17

If we want to cut the maximum likely error in half,we will have to double the sample size.

Question 18

With other factors unchanged,a higher confidence level will require a narrower confidence interval.

Question 19

The difference between the sample statistic and actual value of the population parameter is referred to as the sampling error.

Question 20

An estimator is unbiased if the expected value of the sample statistic is the same as the actual value of the population parameter it is intended to estimate.

Question 21

To use the normal approximation to determine a confidence interval to estimate a population proportion,np and n(1-p)must both be greater than or equal to 5.

Question 22

The sample variance s ² is an unbiased estimator of the population variance $? ^ { 2 }$
when the denominator of s ² is:

A) n + 2.
B) n + 1.
C) n.
D) n - 1.

Question 23

Thirty-six months were randomly sampled and the discount rate on new issues of 91-day Treasury Bills was collected.The sample mean is 4.76% and the standard deviation is 171.21.What is the unbiased estimate for the mean of the population?

A) 29312.86
B) 13.0847
C) 0.0476
D) 4.76%
E) 8.1496

Question 24

Inferential statistics is the:

A) process of using a population parameter to estimate the values for sample statistics.
B) process of using sample statistics to estimate population parameters.
C) process which allows the researcher to determine the exact values for population parameters.
D) process that eliminates the problem of sampling error.
E) branch of statistics involving using population parameters to estimate sampling distributions.

Question 25

The appropriate procedure for constructing an interval estimate for the population mean depends largely on whether the population standard deviation $\text { ? }$
is known.

Question 26

Which of the following statements are correct?

A) A confidence level expresses the degree of certainty that an interval will include the actual value of the population parameter.
B) A confidence level expresses the degree of certainty that a point estimate will include the actual value of the population parameter.
C) A confidence level expresses the degree of certainty that an interval will include the actual value of the sample statistic.
D) A confidence level expresses the degree of certainty that a point estimate will include the actual value of the sample statistic.
E) None of these statements is correct.

Question 27

Accuracy,or sampling error,is equal to one-half of the confidence interval width.

Question 28

An unbiased estimator is:

A) any sample statistic used to approximate a population parameter.
B) a sample statistic,which has an expected value equal to the value of the population parameter.
C) a sample statistic,which is usually less than the population parameter.
D) represented by a sample mean,the sample proportion,the sample variance,and the sample standard deviation.
E) any standard error of the mean or standard error of the proportion.

Question 29

Which of the following statements are correct?

A) A point estimate is an estimate of the range of a population parameter.
B) A point estimate is a single value estimate of the value of a population parameter.
C) A point estimate is an unbiased estimator if its standard deviation is the same as the actual value of the population standard deviation.
D) All of these statements are correct.
E) None of these statements is correct.

Question 30

In developing an interval estimate for a population mean,the population standard deviation $\text { ? }$
was assumed to be 10.The interval estimate was 50.92 $\pm$ 2.14.Had $\text { ? }$
equaled 20,the interval estimate would be:

A) 60.92 $\pm$ 2.14.
B) 50.92 $\pm$ 12.14.
C) 101.84 $\pm$ 4.28.
D) 50.92 $\pm$ 4.28.

Question 31

In developing an interval estimate for a population mean,a sample of 50 observations was used.The interval estimate was 19.76 $\pm$ 1.32.Had the sample size been 200 instead of 50,the interval estimate would have been:

A) 19.76 $\pm$ .33.
B) 19.76 $\pm$ .66.
C) 9.88 $\pm$ 1.32.
D) 4.94 $\pm$ 1.32.

Question 32

In determining the necessary sample size in making an interval estimate for a population mean,it is necessary to decide on the maximum likely error that is acceptable.

Question 33

A sample of 32 orders for a home shopping channel has an average of $78.25.The standard deviation for all orders (the population)is $37.50.A 90% confidence interval around this sample mean would be:

A) $\$ 78.25 \pm \$ 37.50$
B) $\$ 78.25 \pm \$ 10.87$
C) $\$ 78.25 \pm \$ 6.63$
D) $\$ 37.50 \pm \$ 6.63$
E) $\$ 37.50 \pm \$ 1.64$

Question 34

A federal auditor for nationally chartered banks from a random sample of 100 accounts found that the average demand deposit balance at the First National Bank of small town was $549.82.If the auditor needed a point estimate for the population mean for all accounts at this bank,what would she use?

A) The average of $54.98 for this sample.
B) The average of $549.82 for this sample.
C) There is no acceptable value available.
D) She would survey the total of all accounts and determine the mean.
E) Not enough information is given to answer this question.

Question 35

A confidence interval is defined as:

A) a point estimate plus or minus a specific level of confidence.
B) a lower and upper confidence limit associated with a specific level of confidence.
C) an interval that has a 95% probability of containing the population parameter.
D) a lower and upper confidence limit that has a 95% probability of containing the population parameter.
E) the difference between the observed sample statistic and the actual value of the population parameter being estimated.

Question 36

The technique used to determine a confidence interval to estimate a population proportion uses the normal distribution as an approximation to the Poisson distribution.

Question 37

The finite population correction factor will lead to a wider confidence interval than if an infinite population had been assumed.

Question 38

Since the t-interval is often associated with interval estimates based on small samples,it is not appropriate for large samples.

Question 39

A production manager is concerned with the average weight of metal ingots.From past data,she knows that $\text { ? }$
is 1.6 lbs.The manager wishes to make a 95% interval estimate for $\mu$ using a sample of 64 ingots.The accuracy of this sample in estimating the population mean will be:

A) 0.20.
B) 0.392
C) 1.96.
D) 1.6.
E) $\pm$ 0.05.

Question 40

An interval estimate is defined as:

A) the average of the sample values.
B) the range of the sample values.
C) the range of values that are likely to include the actual population parameter.
D) the range of values that are likely to include the actual sample statistic.
E) the population standard deviation.

Question 41

If a sample containing 20 observations is taken from a normally distributed population and a 90% confidence estimate for $\mu$ is needed,the appropriate t-score is:

A) 2.12.
B) 1.746.
C) 2.131.
D) 1.729.
E) 2.602.

Question 42

A total of 150 households were asked if they had Internet access,of which 57 responded "Yes".Which of the following would represent a 98% confidence interval around this sample proportion?

A) $0.380 \mp 2.33$
B) $0.380 \mp 0.092$
C) $0.380 \mp 0.039$
D) $0.380 \mp 0.251$
E) $57 \pm 2.33$

Question 43

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25.The upper limit of a 95% confidence interval for the population mean would equal:

A) 77.769.
B) 72.231.
C) 72.727.
D) 77.273.

Question 44

The larger the level of confidence used in constructing a confidence interval estimate of the population mean the:

A) smaller the probability that the confidence interval will contain the population mean.
B) smaller the value of $Z _ { \alpha / 2 }$
C) wider the confidence interval.
D) narrower the confidence interval.

Question 45

In the formula $\bar { x } \pm z _ { \alpha / 2 } ( ?/ \sqrt { n } )$
,the subscript $( \alpha / 2 )$ refers to the:

A) probability that the confidence interval will contain the population mean.
B) probability that the confidence interval will not contain the population mean.
C) area in the lower tail or upper tail of the sampling distribution of the sample mean.
D) level of confidence.
E) sampling error.

Question 46

The owner of a large shopping center is besieged with complaints concerning the shortage of parking space.He feels that the 1000 spaces are adequate.In an effort to address the problem,he obtains a sample of the average number of cars on the parking lot during prime hours.The sample of 40 has a mean of 952.Assume a population standard deviation of 396.The 95% confidence interval estimate for prime hour parking is:

A) 889.36 to 932.60.
B) 932.60 to 971.40.
C) 829.28 to 1074.72.
D) 849.00 to 1054.99.
E) 952.00 to 1052.00.

Question 47

If a sample containing 12 observations is taken from a normally distributed population and a 99% confidence estimate for $\mu$ is needed,the appropriate t-score is:

A) 2.681.
B) 2.718.
C) 3.169.
D) 3.055.
E) 3.106.

Question 48

A sample of 200 light bulbs was tested and it was found that 11 were defective.Calculate a 95% confidence interval around this sample proportion.

A) $0.055 \pm 1.96$
B) $0.055 \pm 0.016$
C) $0.055 \pm 0.032$
D) $11 \pm 1.96$
E) $200 \pm 11$

Question 49

The lower limit of a confidence interval at the 95% level of confidence for the population proportion if a sample of size 200 had 40 successes is:

A) 0.2554.
B) 0.1446.
C) 0.2465.
D) 0.1535.

Question 50

The national sales manager of Fast Grow Corp is working on next year's budget projections.He knows that the population standard deviation is $17.66.To estimate the daily per diem cost for outside sales people,he has taken a random sample of 36 individual expense accounts and found a mean of $90.29.The 91.08 percent confidence interval for the per diem expense is:

A) 86.45 to 94.13.
B) 60.27 to 120.37.
C) 85.29 to 95.29.
D) 74.43 to 107.9.
E) 84.32 to 96.26.

Question 51

An auditor for a large oil corporation has taken a random sample of monthly credit card charges for 32 individual (non-corporate)accounts.She found a mean of $81.76.Assume that the population standard deviation is 48.2.A 98% confidence interval estimate for the population mean of individual credit card charges would be:

A) 81.7619.89.
B) 81.7616.72.
C) 81.76112.94.
D) 81.7622.0.
E) 81.762.33.

Question 52

A 98% confidence interval estimate for a population mean $\mu$ is determined to be 75.38 to 86.52.If the confidence level is reduced to 90%,the confidence interval for $\mu$ :

A) Becomes wider.
B) Remains the same.
C) Becomes narrower.
D) None of these answers is correct.

Question 53

The t-distribution approaches the normal distribution as the:

A) degrees of freedom increase.
B) degrees of freedom decrease.
C) sample size decreases.
D) population size increases.

Question 54

The security department of a state university is planning its budget for the next year.In estimating the man-hours for security during university sponsored music concerts,the average length of music concerts is needed.A random sample from thirty-six security departments at universities was taken and the sample mean length of concerts was 160 minutes.Suppose the population standard deviation is 45 minutes.A 95 percent confidence interval for the true mean duration of music concerts is:

A) 157.55 to 162.45.
B) 147.63 to 172.37.
C) 71.8 to 248.2.
D) 145.3 to 174.7.
E) 1601.96(45 / 36).

Question 55

Delivery time by courier services is important to stock brokers.One such firm wishes to estimate the average time taken by couriers delivering negotiable securities in New York City.Specifically,the firm randomly samples 36 courier pickup and delivery times.The collected data,in minutes,represent the time between pickup and delivery.Suppose the population standard deviation is 0.3 minutes and the sample mean is 9.975.Find the sample mean and compute.A 90-percent confidence interval for the true mean delivery time, $\mu$ is:

A) 9.852 to 10.05.
B) 119.60 to 119.80.
C) 119.62 to 119.78.
D) 119.26 to 119.87.
E) 9.893 to 10.057.

Question 56

For a sample of size 20 taken from a normally distributed population with standard deviation equal to 5,a 90% confidence interval for the population mean would require the use of:

A) t = 1.328.
B) t = 1.729.
C) z = 1.96.
D) z = 1.645.

Question 57

In order to estimate the average daily down time,a manufacturer randomly samples 40 days of production records and found a mean of 55.576 minutes and standard deviation of 77.9 minutes.An 80% confidence interval is:

A) 55.6751.28(12.32).
B) 55.6751.304(12.32).
C) 55.6751.28(77.9).
D) 55.6751.304(77.9).

Question 58

In an effort to estimate the proportion of female shoppers at a particular store,175 customers were randomly selected,of which 110 were female.Which of the following would represent a 90% confidence interval around this sample proportion?

A) $0.629 \mp 0.072$
B) $110 \mp 1.64$
C) $0.629 \mp 0.036$
D) $0.629 \mp 1.64$
E) $0.629 \mp 0.060$

Question 59

If a sample containing 30 observations is taken from a normally distributed population and a 98% confidence estimate for $\mu$ is needed,the appropriate t-score is:

A) 2.247.
B) 2.756.
C) 2.462.
D) 2.750.
E) 2.330.

Question 60

Your statistics instructor wants you to determine a confidence interval estimate for the mean test score for the next exam.In the past,the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9.A 95% confidence interval estimate if your class has 30 students is:

A) 68.72 to 79.68.
B) 13.64 to 134.76.
C) 64.92 to 83.48.
D) 62.66 to 85.73.
E) 63.14 to 85.26.

Question 61

You are interested in determining the average cost of a 3-minute telephone call to locations within the continental U.S.What sample size must you take to be 96% confident that the results will be within $.75 of the true mean cost per call? From the phone company,you have gotten an estimate of $\text { ? }$
= 7.71.

A) 185
B) 445
C) 406
D) 574
E) 22

Question 62

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old.How large a sample size must be taken to make an estimate of the true proportion of citizens who favor this move.The error should be no more than 0.01 with 99% confidence.

A) 167
B) 16641
C) 6450
D) 65
E) 1670

Question 63

In surveying a simple random sample of 1000 assistant professors,we found that 573 of them felt they were underpaid by at least $3500.Based on these results,we have a 95% confidence that the proportion of the population of assistant professors who share this sentiment is between .548 and .598.
Identify the point estimate of the population proportion.

Question 64

A medical records manager would like to review hospital records in order to determine the average hospital stay for surgery patients during the past year.What sample size must be taken in order to be 95% confident that the estimate is within 1 day of the true mean? She has past studies,which indicate that is 20.25 days.

Question 65

U.S.News and World Report each year conducts a survey of starting salaries in various career fields.If you were to devise a plan to replicate this study,how large a sample would you need to take to be 98% certain that your estimate is within $500 of the true mean starting salary? Assume that is $3500.

Question 66

The Ford Motor Company is interested in consumer acceptance of its subcompact car based on the proportion of positive responses to a survey.How large a survey must the company take to have 95% confidence and no more than 0.01 error?

A) 19208
B) 9604
C) 49
D) 4900
E) 9603

Question 67

Because of the popularity of movies as an entertainment medium for college students,you plan to do a national study of the average cost of a movie ticket.If you assume that $\text { ? }$
= $0.50,what sample size would you have to take to be 95% confident that your estimate was within $0.25 of the true mean ticket prices?

A) 15
B) 7
C) 8
D) 4
E) 16

Question 68

A simple random sample of 10 students is selected from a large college.For the 10 students,the number of days each was absent during the last semester was to be 3,7,2,1,0,2,4,2,6,and 2.What is the point estimate for the mean number of days absent for the college's students?

Question 69

In surveying a simple random sample of 1000 assistant professors,we found that 573 of them felt they were underpaid by at least $3500.Based on these results,we have a 90% confidence that the proportion of the population of assistant professors who share this sentiment is between .548 and .598.
Identify the accuracy of the sample result.
The sample proportion would not differ from the actual population proportion by more than:

Question 70

The banking industry has suffered in recent years because of a high default rate on energy-related loans.The standard deviation is $10,000.How large a sample must you take from banking records to be 98% confident that your estimate for the amount of these defaults is within $1000 of the true mean loan amount?

A) 567
B) 233
C) 240
D) 543
E) 890

Question 71

A simple random sample of 10 students is selected from a large college.For the 10 students,the number of days each was absent during the last semester was to be 3,7,2,1,0,2,4,2,6,and 2.What is the point estimate for ,the variance of the number of days absent for the college's students?

Question 72

A large bank in a metropolitan area has a large number of secured loans on apartment facilities throughout the area.Local economic indicators suggest the percentage of vacant apartments ranges from 7% to 10%.Concerned about the borrowers' ability to meet loan obligations on time the bank decides to sample from the apartments used to secure loans.The officer responsible for the sample decides to allow a maximum error of the estimate of 0.01 with 99 percent confidence.The officer wishes to take a sample large enough to cover all proportions within the estimated vacancy range.Compute the sample size needed for this study.

Question 73

Coffee for breakfast in the 1960's was a commonplace method of becoming more alert for classes among college students.However,coffee makers have seen a decline in U.S.coffee consumption and are obviously concerned about it.One coffee maker decides to estimate the proportion of college students (likely candidates for coffee)who drink coffee for breakfast nationally.The proportion of the total population who drink coffee for breakfast is about 0.55.The coffee maker decides to use 0.55 as the value for p in determining the sample size to select from among college students.A 92% confidence interval is chosen and the estimate,p,is to be within 0.05 of the true proportion of college students who drink coffee for breakfast.Compute the needed sample size.

Question 74

A simple random sample of 10 students is selected from a large college.For the 10 students,the number of days each was absent during the last semester was to be 3,7,2,1,0,2,4,2,6,and 2.What is the point estimate for ,the standard deviation of the number of days absent for the college's students?

Question 75

An auditor wishes to take a sample to verify the accounts receivable balances for a very large corporation.From past history,he knows that is $102.49.What sample size must be taken to be 99% confident that the estimate will be within $5 of the true mean account balance?

Question 76

The Arkansas State Police wish to estimate the average mph being traveled on the Interstate Highways,which cross the state.If the estimate is to be within 8 mpg of the true mean with 98% confidence and the estimated standard deviation is 22 mph,how large a sample size must be taken?

A) 42
B) 15
C) 329
D) 14
E) 41

Question 77

A cost accountant wished to establish the average amount, ,spent by executives per day on travel and lodging.Then a comparison,between the average and the amount turned in to be reimbursed,will be made and unreasonably high or low expense amounts audited.A random sample of 50 executive expense receipts is taken.The average in the sample was $208.From a similar survey the standard deviation of the amounts is approximately = $29.The accountant prepares a 90-percent confidence level for .What is its maximum error?

Question 78

A fund raiser for United Way wants to know the average annual income of workers in a very large vegetable processing plant.She is able to obtain a sample of 30 annual wage levels (in thousands).She finds that the summation of the wages for the 30 is 370.7 and the standard deviation of 3.3.What estimate may be used for ?

Question 79

An auditor wishes to take a sample to verify the accounts receivable balances for a company having 500 accounts.From past history,he knows that is $102.49.What sample size must be taken to be 99% confident that the estimate will be within $10 of the true mean account balance?

Question 80

Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean?

A) A point estimate of the population mean
B) The standard error of the sampling distribution of the sample mean
C) The confidence level
D) The value of the population mean
E) The sample size