Deck 8: Statistical Inference: Estimation for Single Populations

Question 1

Estimate the population mean with a known population standard deviation with the z statistic,correcting for a finite population if necessary.

Answer 1

At times in business research,a product is new or untested or information about the population is unknown.In such cases,gathering data from a sample and making estimates about the population is useful and can be done with a point estimate or an interval estimate.A point estimate is the use of a statistic from the sample as an estimate for a parameter of the population.Because point estimates vary with each sample,it is usually best to construct an interval estimate.An interval estimate is a range of values computed from the sample within which the researcher believes with some confidence that the population parameter lies.Certain levels of confidence seem to be used more than others: 90%,95%,98%,and 99%.

Question 2

When the population standard deviation,σ,is unknown the sample standard deviation,s,is used in determining the interval estimate for the population mean.

Answer 2

True

Question 3

If the population is normal and its standard deviation,σ,is unknown and the sample size,n,is large (n ≥ 30),interval estimates for the population mean must be determined using z values.

Answer 3

False

Question 4

If the population is normal and its standard deviation,σ,is known but the sample size is small,z-distribution values may not be used to determine interval estimates for the population mean.

Question 5

Estimate a population proportion using the z statistic.

Question 6

In determining the interval estimates for a population variance using the sample variance,it is appropriate to use the values from a chi-square distribution rather than a t distribution.

Question 7

A t distribution is similar to a normal distribution,but flatter in the middle.

Question 8

In estimating the sample size necessary to estimate a population mean,the error of estimation,E,is equal to the difference between the sample mean and the population mean.

Question 9

In order to find values in the t distribution table,you must determine the appropriate degrees of freedom based on the sample sizes.

Question 10

If the degrees of freedom in a t distribution increase,difference between the t values and the z values will also increase.

Question 11

When a statistic calculated from sample data is used to estimate a population parameter,it is called a point estimate.

Question 12

Use of the chi-square statistic to estimate the population variance is extremely robust to the assumption that the population is normally distributed.

Question 13

If the population is not normal but its standard deviation,σ,is known and the sample size,n is large (n ≥ 30),z-distribution values may be used to determine interval estimates for the population mean.

Question 14

Use the chi-square distribution to estimate the population variance given the sample variance.

Question 15

An assumption underlying the use of t statistic in sample-based estimation is that the population is normally distributed.

Question 16

Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.

Question 17

Like a t distribution,a chi-square distribution is symmetrical and extends from minus infinity to plus infinity.

Question 18

Determine the sample size needed in order to estimate the population mean and population proportion.

Question 19

When a range of values is used to estimate a population parameter,it is called a range estimate.

Question 20

In determining the interval estimates for a population proportion using the sample proportion,it is appropriate to use the values from a t distribution rather than the z distribution.

Question 21

A random sample of 64 items is selected from a population of 400 items.The sample mean is 200.The population standard deviation is 48.From this data,a 95% confidence interval to estimate the population mean can be computed as ___.

A)189.21 to 210.79
B)188.24 to 211.76
C)190.13 to 209.87
D)190.94 to 209.06
E)193.45 to 211.09

Question 22

Brian Vanecek,VP of Operations at Portland Trust Bank,is evaluating the service level provided to walk-in customers.Accordingly,his staff recorded the waiting times for 45 randomly selected walk-in customers,and calculated that their mean waiting time was 15 minutes.If Brian concludes that the average waiting time for all walk-in customers is 15 minutes,he is using a ___.

A)a range estimate
B)a statistical parameter
C)an interval estimate
D)a point estimate
E)an exact estimate

Question 23

Brian Vanecek,VP of Operations at Portland Trust Bank,is evaluating the service level provided to walk-in customers.Accordingly,his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes.Assume that the population standard deviation is 4 minutes.The 90% confidence interval for the population mean of waiting times is ___.

A)14.27 to 15.73
B)14.18 to 15.82
C)9.88 to 20.12
D)13.86 to 16.14
E)18.12 to 19.87

Question 24

The z value associated with a two-sided 90% confidence interval is ___.

A)1.28
B)1.645
C)1.96
D)2.575
E)2.33

Question 25

The z value associated with a two-sided 80% confidence interval is ___.

A)1.645
B)1.28
C)0.84
D)0.29
E)2.00

Question 26

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of a new toothpaste package.Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs.If Catherine concludes that 17% of all households prefer the new package,she is using a ___.

A)a point estimate
B)a range estimate
C)a statistical parameter
D)an interval estimate
E)an exact estimate

Question 27

James Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 100 workers in New Brunswick and determined that their mean training time was 25 hours.Assume that the population standard deviation is 5 hours.The 92% confidence interval for the population mean of training times is ___.

A)16.25 to 33.75
B)24.30 to 25.71
C)17.95 to 32.05
D)24.13 to 25.88
E)24.45 to 27.32

Question 28

James Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 100 workers in New Brunswick and determined that their mean training time was 25 hours.Assume that the population standard deviation is 5 hours.The 95% confidence interval for the population mean of training times is ___.

A)15.20 to 34.80
B)24.18 to 25.82
C)24.02 to 25.98
D)16.78 to 33.23
E)23.32 to 35.46

Question 29

Suppose a random sample of 36 is selected from a population with a standard deviation of 12.If the sample mean is 98,the 90% confidence interval for the population mean is ___.

A)94.71 to 101.29
B)97.45 to 98.55
C)94.08 to 101.92
D)97.35 to 98.65
E)95.00 to 105.00

Question 30

Suppose a random sample of 36 is selected from a population with a standard deviation of 12.If the sample mean is 98,the 99% confidence interval to estimate the population mean is ___.

A)94.08 to 101.92
B)92.85 to 103.15
C)97.35 to 98.65
D)93.34 to 102.66
E)90.20 to 105.00

Question 31

Suppose a random sample of size 64 is selected from a population yielding a sample mean of 26.The population standard deviation is 4.From this information,the 90% confidence interval to estimate the population mean can be computed to be ___.

A)25.36 to 26.64
B)25.92 to 26.08
C)25.18 to 26.82
D)25.90 to 26.10
E)26.00 to 27.80

Question 32

The table t value associated with the upper 5% of the t distribution and 12 degrees of freedom is ___.

A)2.179
B)1.782
C)1.356
D)3.055
E)3.330

Question 33

A random sample of 64 items is selected from a population of 400 items.The sample mean is 200.The population standard deviation is 48.From this data,a 90% confidence interval to estimate the population mean can be computed as ___.

A)189.21 to 210.79
B)188.24 to 211.76
C)190.13 to 209.87
D)190.94 to 209.06
E)193.45 to 211.09

Question 34

The z value associated with a two-sided 88% confidence interval is ___.

A)1.28
B)1.555
C)1.17
D)0.88
E)1.90

Question 35

The table t value associated with the upper 5% of the t distribution and 14 degrees of freedom is ___.

A)2.977
B)2.624
C)2.145
D)1.761

Question 36

Eugene Gates,Marketing Director of Mansfield Motors Manufacturers,Inc.'s Electrical Division,is leading a study to assess the relative importance of product features.An item on a survey questionnaire distributed to 100 of Mansfield's customers asked them to rate the importance of "ease of maintenance" on a scale of 1 to 10 (with 1 meaning "not important" and 10 meaning "highly important").His staff assembled the following statistics: If Eugene concludes that the average rate of "ease of maintenance" for all customers is 7.5,he is using ___.

A)a range estimate
B)a statistical parameter
C)a point estimate
D)an interval estimate
E)a guesstimate

Question 37

James Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 100 workers in New Brunswick and determined that their mean training time was 25 hours.Assume that the population standard deviation is 5 hours.The 88% confidence interval for the population mean of training times is ___.

A)17.25 to 32.75
B)24.23 to 25.78
C)24.42 to 25.59
D)19.15 to 30.85
E)21.00 t0 32.00

Question 38

Brian Vanecek,VP of Operations at Portland Trust Bank,is evaluating the service level provided to walk-in customers.Accordingly,his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes.Assume that the population standard deviation is 4 minutes.The 95% confidence interval for the population mean of waiting times is ___.

A)14.02 to 15.98
B)7.16 to 22.84
C)14.06 to 15.94
D)8.42 to 21.58
E)19.80 to 23.65

Question 39

The normal distribution is used to test about a population mean for large samples if the population standard deviation is known."Large" is usually defined as ___.

A)at least 10
B)at least 5% of the population size
C)at least 30
D)at least 12
E)at least 100

Question 40

The z value associated with a two-sided 95% confidence interval is ___.

A)1.28
B)1.645
C)1.96
D)2.575
E)2.33

Question 41

A researcher wants to estimate the proportion of a population which possesses a given characteristic.A random sample of size 250 is taken and 40% of the sample possesses the characteristic.The 95% confidence interval to estimate the population proportion is ___.

A)0.35 to 0.45
B)0.34 to 0.46
C)0.37 to 0.43
D)0.39 to 0.41
E)0.40 to 0.42

Question 42

A researcher wants to estimate the proportion of the population which possesses a given characteristic.A random sample of size 800 is taken resulting in 360 items which possess the characteristic.The point estimate for this population proportion is ___.

A)0.55
B)0.45
C)0.35
D)0.65
E)0.70

Question 43

Elwin Osbourne,CIO at GFS,Inc. ,is studying employee use of GFS email for non-business communications.A random sample of 200 email messages was selected.Thirty of the messages were not business related.The 95% confidence interval for the population proportion is ___.

A)0.108 to 0.192
B)0.153 to 0.247
C)0.091 to 0.209
D)0.101 to 0.199
E)0.199 to 0.201

Question 44

A researcher is interested in estimating the mean value for a population.She takes a random sample of 17 items and computes a sample mean of 224 and a sample standard deviation of 32.She decides to construct a 98% confidence interval to estimate the mean.The degrees of freedom associated with this problem are ___.

A)18
B)17
C)16
D)15
E)20

Question 45

A researcher wants to estimate the proportion of a population which possesses a given characteristic.A random sample of size 200 is taken and 30% of the sample possesses the characteristic.The 95% confidence interval to estimate the population proportion is ___.

A)0.53 to 0.67
B)0.25 to 0.35
C)0.24 to 0.36
D)0.27 to 0.33
E)0.28 to 0.34

Question 46

The weights of aluminum castings produced by a process are normally distributed.A random sample of 5 castings is selected;the sample mean weight is 2.21 kilograms;and the sample standard deviation is 0.12 kilograms.The 98% confidence interval for the population mean casting weight is ___.

A)1.76 to 2.66
B)2.01 to 2.41
C)2.08 to 2.34
D)1.93 to 2.49
E)2.49 to 2.67

Question 47

Life tests performed on a sample of 13 batteries of a new model indicated: (1)an average life of 75 months,and (2)a standard deviation of 5 months.Other battery models,produced by similar processes,have normally distributed life spans.The 90% confidence interval for the population mean life of the new model is ___.

A)66.78 to 83.23
B)72.72 to 77.28
C)72.53 to 77.47
D)66.09 to 83.91
E)73.34 to 76.25

Question 48

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of a new toothpaste package.She randomly selects a sample of 200 households.Forty households prefer the new package to all other package designs.The point estimate for this population proportion is ___.

A)0.20
B)0.25
C)0.40
D)0.45
E)0.55

Question 49

A researcher wants to estimate the proportion of a population which possesses a given characteristic.A random sample of size 200 is taken and 30% of the sample possesses the characteristic.The 90% confidence interval to estimate the population proportion is ___.

A)0.53 to 0.67
B)0.25 to 0.35
C)0.24 to 0.36
D)0.27 to 0.33
E)0.33 to 0.39

Question 50

The lengths of steel rods produced by a shearing process are normally distributed.A random sample of 10 rods is selected;the sample mean length is 119.05 centimetres;and the sample standard deviation is 0.10 centimetres.The 95% confidence interval for the population mean rod length is ___.

A)118.99 to 119.11
B)118.82 to 119.28
C)118.98 to 119.12
D)118.85 to 119.25
E)119.89 to 122.12

Question 51

The table t value associated with the upper 10% of the t distribution and 23 degrees of freedom is ___.

A)1.319
B)1.714
C)2.069
D)1.321
E)2.332

Question 52

A random sample of 225 items from a population results in 60% possessing a given characteristic.Using this information,the researcher constructs a 90% confidence interval to estimate the population proportion.The resulting confidence interval is ___.

A)0.546 to 0.654
B)0.536 to 0.664
C)0.596 to 0.604
D)0.571 to 0.629
E)0.629 to 0.687

Question 53

Elwin Osbourne,CIO at GFS,Inc. ,is studying employee use of GFS email for non-business communications.A random sample of 200 email messages was selected.Thirty of the messages were not business related.The 98% confidence interval for the population proportion is ___.

A)0.108 to 0.192
B)0.153 to 0.247
C)0.091 to 0.209
D)0.145 to 0.255
E)0.250 to 0.275

Question 54

Life tests performed on a sample of 13 batteries of a new model indicated: (1)an average life of 75 months,and (2)a standard deviation of 5 months.Other battery models,produced by similar processes,have normally distributed life spans.The 98% confidence interval for the population mean life of the new model is ___.

A)63.37 to 86.63
B)61.60 to 88.41
C)71.77 to 78.23
D)71.28 to 78.72
E)79.86 to 81.28

Question 55

Elwin Osbourne,CIO at GFS,Inc. ,is studying employee use of GFS email for non-business communications.A random sample of 200 email messages was selected.Thirty of the messages were not business related.The 90% confidence interval for the population proportion is ___.

A)0.108 to 0.192
B)0.153 to 0.247
C)0.091 to 0.209
D)0.145 to 0.255
E)0.255 to 0.265

Question 56

A researcher wants to estimate the proportion of the population which possesses a given characteristic.A random sample of size 1800 is taken resulting in 450 items which possess the characteristic.The point estimate for this population proportion is ___.

A)0.55
B)0.45
C)0.35
D)0.25
E)0.15

Question 57

Elwin Osbourne,CIO at GFS,Inc. ,is studying employee use of GFS email for non-business communications.A random sample of 200 email messages was selected.Thirty of the messages were not business related.The point estimate for this population proportion is ___.

A)0.150
B)0.300
C)0.182
D)0.667
E)0.786

Question 58

A random sample of 225 items from a population results in 60% possessing a given characteristic.Using this information,the researcher constructs a 99% confidence interval to estimate the population proportion.The resulting confidence interval is ___.

A)0.54 to 0.66
B)0.59 to 0.61
C)0.57 to 0.63
D)0.52 to 0.68
E)0.68 to 0.76

Question 59

The lengths of steel rods produced by a shearing process are normally distributed.A random sample of 10 rods is selected;the sample mean length is 119.05 centimetres;and the sample standard deviation is 0.10 centimetres.The 90% confidence interval for the population mean rod length is ___.

A)118.99 to 119.11
B)118.87 to 119.23
C)119.00 to 119.10
D)118.89 to 119.21
E)119.21 to 123.87

Question 60

A researcher wants to estimate the proportion of a population which possesses a given characteristic.A random sample of size 250 is taken and 40% of the sample possesses the characteristic.The 90% confidence interval to estimate the population proportion is ___.

A)0.35 to 0.45
B)0.34 to 0.46
C)0.37 to 0.43
D)0.39 to 0.41
E)0.40 to 0.45

Question 61

A study will be conducted to estimate the population proportion.A level of confidence of 99% will be used and an error of no more than .04 is desired.There is no knowledge as to what the population proportion will be.The size of sample should be at least ___.

A)1037
B)160
C)41
D)259
E)289

Question 62

Given n = 20,s = 32,and that the population is normally distributed,the 90% confidence interval for the population variance is ___.

A)645.4460 $\le$ $\sigma$ ² $\le$ 1923.0978
B)599.3635 $\le$ $\sigma$ ² $\le$ 2135.3859
C)592.2258 $\le$ $\sigma$ ² $\le$ 2184.4685
D)652.0129 $\le$ $\sigma$ ² $\le$ 1887.4185
E)642.0929 $\le$ $\sigma$ ² $\le$ 3982.2989

Question 63

A study is going to be conducted in which a population mean will be estimated using a 92% confidence interval.The estimate needs to be within 12 of the actual population mean.The population variance is estimated to be around 2500.The necessary sample size should be at least ___.

A)15
B)47
C)54
D)638
E)700

Question 64

Given n = 12,s² = 44.90,and that the population is normally distributed,the 99% confidence interval for the population variance is ___.

A)19.0391 $\le$ $\sigma$ ² $\le$ 175.2888
B)23.0881 $\le$ $\sigma$ ² $\le$ 122.3495
C)25.6253 $\le$ $\sigma$ ² $\le$ 103.0993
D)18.4588 $\le$ $\sigma$ ² $\le$ 189.7280
E)14.2929 $\le$ $\sigma$ ² $\le$ 139.2989

Question 65

James Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 10 workers in Nova Scotia,and determined that their mean training time was 25 hours and that the standard deviation was 5 hours.Assume that training times are normally distributed.The 90% confidence interval for the population variance of training times is ___.

A)11.83 to 83.33
B)2.37 to 16.67
C)2.66 to 13.51
D)13.30 to 67.67
E)15.00 to 68.00

Question 66

A researcher conducts a study to determine what the population proportion is for a given characteristic.It is believed from previous studies that the proportion of the population will be at least .65.The researcher wants to use a 98% level of confidence.He also wants the error to be no more than .03.The sample size should be at least ___.

A)41
B)313
C)1677
D)1373
E)1500

Question 67

Velma Vasquez,fund manager of the Vasquez Value Fund,manages a portfolio of 250 common stocks.Velma relies on various statistics,such as variance,to assess the overall risk of stocks in an economic sector.Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%.Assume that annualized returns are normally distributed.The 90% confidence interval for the population variance of annualized returns is ___.

A)0.018 to 0.064
B)0.016 to 0.078
C)0.017 to 0.066
D)0.016 to 0.075
E)0.020 to 0.080

Question 68

James Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 10 workers in Nova Scotia,and determined that their mean training time was 25 hours and that the standard deviation was 5 hours.Assume that training times are normally distributed.The 95% confidence interval for the population variance of training times is ___.

A)11.83 to 83.32
B)2.37 to 16.67
C)2.66 to 13.51
D)13.30 to 67.67
E)15.40 to 68.28

Question 69

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of a new toothpaste package.She plans to use a 95% confidence interval estimate of the proportion of households which prefer the new packages;she will accept a 0.05 error.Previous studies indicate that new packaging has an approximately 70% acceptance rate.The sample size should be at least ___.

A)27
B)59
C)323
D)427
E)500

Question 70

Given n = 17,s² = 18.56,and that the population is normally distributed,the 80% confidence interval for the population variance is ___.

A)11.4372 $\le$ $\sigma$ ² $\le$ 36.3848
B)23.5418 $\le$ $\sigma$ ² $\le$ 9.31223
C)12.6141 $\le$ $\sigma$ ² $\le$ 31.8892
D)11.2929 $\le$ $\sigma$ ² $\le$ 37.2989
E)14.2929 $\le$ $\sigma$ ² $\le$ 39.2989

Question 71

Brian Vanecek,VP of Operations at Portland Trust Bank,is evaluating the service level provided to walk-in customers.Brian would like to minimize the variance of waiting time for these customers,since this would mean each customer received the same level of service.Accordingly,his staff recorded the waiting times for 15 randomly selected walk-in customers,and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes.Assume that waiting time is normally distributed.The 95% confidence interval for the population variance of waiting times is ___.

A)9.46 to 34.09
B)56.25 to 64.87
C)11.05 to 16.03
D)8.58 to 39.80
E)12.50 to 42.35

Question 72

Elwin Osbourne,CIO at GFS,Inc. ,is studying employee use of GFS email for non-business communications.He plans to use a 98% confidence interval estimate of the proportion of email messages that are non-business;he will accept a 0.05 error.Previous studies indicate that approximately 30% of employee email is not business related.Elwin should sample ___ email messages.

A)323
B)12
C)457
D)14
E)100

Question 73

In estimating the sample size necessary to estimate p,if there is no good approximation for the value of p available,the value of ___ should be used as an estimate of p in the formula.

A)0.10
B)0.50
C)0.40
D)1.96
E)2.00

Question 74

A researcher wants to estimate the population proportion with a 95% level of confidence.He estimates from previous studies that the population proportion is no more than .30.The researcher wants the estimate to have an error of no more than .03.The necessary sample size is at least ___.

A)27
B)188
C)211
D)897
E)900

Question 75

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of a new toothpaste package.She randomly selects a sample of 200 households.Forty households prefer the new package to all other package designs.The 90% confidence interval for the population proportion is ___.

A)0.199 to 0.201
B)0.153 to 0.247
C)0.164 to 0.236
D)0.145 to 0.255
E)0.185 to 0.275

Question 76

A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points.The range of population values is 80 and the researcher plans to use a 90% level of confidence.The sample size should be at least ___.

A)44
B)62
C)216
D)692
E)700

Question 77

A researcher wants to estimate the population proportion with a 90% level of confidence.She estimates from previous studies that the population proportion is no more than .30.The researcher wants the estimate to have an error of no more than .02.The necessary sample size is at least ___.

A)29
B)47
C)298
D)1421
E)1500

Question 78

Elwin Osbourne,CIO at GFS,Inc. ,is studying employee use of GFS email for non-business communications.He plans to use a 95% confidence interval estimate of the proportion of email messages that are non-business;he will accept a 0.05 error.Previous studies indicate that approximately 30% of employee email is not business related.Elwin should sample ___ email messages.

A)323
B)12
C)457
D)14
E)100

Question 79

Brian Vanecek,VP of Operations at Portland Trust Bank,is evaluating the service level provided to walk-in customers.Brian would like to minimize the variance of waiting time for these customers,since this would mean each customer received the same level of service.Accordingly,his staff recorded the waiting times for 15 randomly selected walk-in customers,and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes.Assume that waiting time is normally distributed.The 90% confidence interval for the population variance of waiting times is ___.

A)9.46 to 34.09
B)56.25 to 64.87
C)11.05 to 16.03
D)8.58 to 39.79
E)12.50 to 42.35

Question 80

Velma Vasquez,fund manager of the Vasquez Value Fund,manages a portfolio of 250 common stocks.Velma relies on various statistics,such as variance,to assess the overall risk of stocks in an economic sector.Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%.Assume that annualized returns are normally distributed.The 95% confidence interval for the population variance of annualized returns is ___.

A)0.018 to 0.064
B)0.016 to 0.078
C)0.017 to 0.066
D)0.016 to 0.075
E)0.020 to 0.080