Deck 7: Estimation: Single Population

Question 1

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes.A random sample of 75 patients in the local hospital had a mean time of 90 minutes.Assume a 95% confidence interval for the population mean μ.
What is the formula used to calculate the standard error?

A)σ /
B)σ² /
C)σ / n
D)σ / n²

Answer 1

σ /

Question 2

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes.A random sample of 75 patients in the local hospital had a mean time of 90 minutes.Assume a 95% confidence interval for the population mean μ.
Calculate the margin of error of the 95% confidence interval.

A)5.69
B)8.93
C)6.79
D)8.06

Answer 2

6.79

Question 3

Find the lower confidence limit of the 99% confidence interval.

A)340.25
B)325.98
C)319.59
D)332.41

Answer 3

319.59

Question 4

Let X₁,X₂,X₃,and X₄ be a random sample of observations from a population with mean μ and variance σ².Consider the following estimator of μ: ₁ = 0.15 X₁ + 0.35 X₂ + 0.20 X₃ + 0.30 X₄.What is the variance of
₁?

A)0)20 σ²
B)0)275 σ²
C)0)55 σ²
D)0)125 σ²

Question 5

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Consider the following point estimators,W,X,Y,and Z of μ: W = (x₁ + x₂)/2;
X = (2x₁ + x₂)/3;Y = (x₁ + 3x₂)/4;and Z = (2x₁ + 3x₂)/5.
Which of the following point estimators is the most efficient?

A)W
B)X
C)Y
D)Z

Question 6

The number of television sets produced from an assembly line each day is known to have a standard deviation of 17.4 sets per day.The production line averaged 452.3 sets per day for 20 randomly selected days.Which of the following represents a 95% confidence interval for the population mean number of sets per hour?

A)452.3 ± 9.4
B)452.3 + 11.3
C)452.3 ± 13.8
D)452.3 ± 7.63

Question 7

In a recent survey of 600 adults,16.4% indicated that they had fallen asleep in front of the television in the past month.Which of the following intervals represents a 98% confidence interval for the population proportion?

A)0.137 to 0.192
B)0.140 to 0.189
C)0.129 to 0.199
D)0.143 to 0.186

Question 8

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes.A random sample of 75 patients in the local hospital had a mean time of 90 minutes.Assume a 95% confidence interval for the population mean μ.
Calculate the standard error of the 95% confidence interval.

A)0.40
B)3.46
C)13.69
D)2.50

Question 9

What is the relative efficiency of W with respect to X?

A)0.9
B)1.6
C)1.1
D)0.4

Question 10

Which of the following statements is true regarding the width of a confidence interval for a population proportion?

A)It is narrower for 95% confidence than for 90% confidence.
B)It is wider for a sample of size 80 than for a sample of size 40.
C)It is wider for 95% confidence than for 99% confidence.
D)It is narrower when the sample proportion is 0.20 than when the sample proportion is 0.50.

Question 11

Find the upper confidence limit of the 99% confidence interval.

A)340.25
B)325.98
C)319.59
D)332.41

Question 12

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of beverage cans produced each hour from a vending machine is normally distributed with a standard deviation of 8.6.For a random sample of 12 hours,the average number of beverage cans produced was 326.0.Assume a 99% confidence interval for the population mean number of beverage cans produced per hour.
Calculate the width of the 99% confidence interval estimate.

A)12.81
B)3.21
C)6.41
D)7.20

Question 13

The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet.For a random sample of 15 sails,the mean amount of material used is 912 square feet.Which of the following represents a 99% confidence interval for the population mean amount of material used in a custom sail?

A)912 ± 49.2
B)912 ± 42.6
C)912 ± 44.3
D)912 ± 46.8

Question 14

The manager of the local health club is interested in determining the number of times members use the weight room per month.She takes a random sample of 15 members and finds that over the course of a month,the average number of visits was 11.2 with a standard deviation of 3.2.Assuming that the monthly number of visits is normally distributed,which of the following represents a 95% confidence interval for the average monthly usage of all health club members?

A)11.2 ± 1.74
B)11.2 ± 1.77
C)11.2 ± 1.62
D)11.2 ± 1.83

Question 15

The dollar value of orders placed through a particular store catalog is found to be normally distributed with a standard deviation of $21.58.A sample of 30 orders averaged $81.25.What is the 90% confidence interval around this sample mean?

A)$81.25 ± $21.58
B)$81.25 ± $10.79
C)$81.25 ± $12.15
D)$81.25 ± $6.48

Question 16

In a survey of 472 personnel directors,63% thought that they would be hiring new personnel over the next three months.Which of the following represents a 98% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months?

A)0.63 ± 0.057
B)0.63 ± 0.047
C)0.63 ± 0.042
D)0.63 ± 0.052

Question 17

For a population that is normally distributed with a very large population size compared to the sample size,the variance of the sample mean is given by:

A)σ /
B)σ² /
C)σ / n
D)σ² / n

Question 18

What is the relative efficiency of Z with respect to Y?

A)0.50
B)0.80
C)1.20
D)1.50

Question 19

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of beverage cans produced each hour from a vending machine is normally distributed with a standard deviation of 8.6.For a random sample of 12 hours,the average number of beverage cans produced was 326.0.Assume a 99% confidence interval for the population mean number of beverage cans produced per hour.
Calculate the margin of error of the 99% confidence interval.

A)1.85
B)3.60
C)6.41
D)10.56

Question 20

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes.A random sample of 75 patients in the local hospital had a mean time of 90 minutes.Assume a 95% confidence interval for the population mean μ.
Calculate the width of the 95% confidence interval estimate.

A)16.12
B)11.38
C)17.86
D)13.58

Question 21

In developing an interval estimate for a population mean,the population standard deviation σ is assumed to be 8.The interval estimate is 45.82 ± 2.36.What will be the interval estimate for the population mean if σ is equal to 16?

A)45.82 ± 4.72
B)45.82 ± 2.36
C)45.82 ± 9.44
D)45.82 ± 5.56

Question 22

If a sample of size 30 is selected,the value of A for the probability P(t ≥A)= 0.01 is:

A)2.247
B)2.045
C)2.462
D)2.750

Question 23

If a sample has 20 observations and a 90% confidence estimate for μ is needed,the appropriate t-score is:

A)2.120
B)1.746
C)2.131
D)1.729

Question 24

Which of the following distributions is used when estimating the population mean from a normal population with unknown variance?

A)the t distribution with n + 1 degrees of freedom
B)the t distribution with n degrees of freedom
C)the t distribution with n - 1 degrees of freedom
D)the t distribution with 2n degrees of freedom

Question 25

Which of the following statements is true?

A)If a sample has 16 observations and a 90% confidence estimate for μ is needed,the appropriate t-score is 1.753.
B)If a sample has 16 observations and a 99% confidence estimate for μ is needed,the appropriate t-score is 2.602.
C)If a sample has 20 observations and a 95% confidence estimate for μ is needed,the appropriate t-score is 1.729.
D)If a sample has 20 observations and a 98% confidence estimate for μ is needed,the appropriate t-score is 2.093.

Question 26

A 95% confidence interval estimate for a population mean μ is determined to be 65.48 to 76.52.Which of the following is true if a 90% confidence interval for μ is constructed?

A)It is wider than the 95% confidence interval.
B)It is the same as the 95% confidence interval.
C)It is narrower than the 95% confidence interval.
D)There is not enough information to determine the answer.

Question 27

The 95% confidence interval for the population proportion P,given a sample size n = 2200 and sample proportion = 0.214 is computed as:

A)0.214 ± 0.017
B)0.214 ± 0.048
C)0.214 ± 0.069
D)0.214 ± 0.086

Question 28

Find the upper confidence limit of the 95% confidence interval.

A)95.68
B)98.07
C)96.79
D)94.43

Question 29

The lower limit of a 95% confidence interval for the population proportion P given a sample size n = 100 and sample proportion = 0.62 is equal to:

A)0.715
B)0.699
C)0.525
D)0.440

Question 30

If a sample of size 200 has 40 successes,the lower limit of a confidence interval at the 95% level of confidence for the population proportion is:

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

Question 31

Find the upper confidence limit of the 90% confidence interval.

A)13.81
B)18.24
C)21.59
D)25.89

Question 32

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A school bus driver records the time (in minutes)it takes to commute to school for six days.Those results are: 25,22,17,20,15,and 10.Assuming the population is normally distributed,develop a 90% confidence interval for the population mean.
What is the value of the sample standard deviation?

A)4.88
B)4.25
C)5.34
D)3.64

Question 33

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A school bus driver records the time (in minutes)it takes to commute to school for six days.Those results are: 25,22,17,20,15,and 10.Assuming the population is normally distributed,develop a 90% confidence interval for the population mean.
What is the value of the sample mean?

A)22.6
B)20.4
C)16.8
D)18.2

Question 34

Find the lower confidence limit of the 90% confidence interval.

A)13.81
B)18.24
C)22.59
D)25.89

Question 35

In developing an interval estimate for a population mean,a sample of 40 observations was used.The interval estimate was 28.76 ± 1.48.Had the sample size been 160 instead of 40,the interval estimate would have been:

A)28.76 ± 0.37
B)28.76 ± 0.74
C)28.76 ± 1.48
D)28.76 ± 2.96

Question 36

Find the lower confidence limit of the 95% confidence interval.

A)83.21
B)85.57
C)81.93
D)84.32

Question 37

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A school bus driver records the time (in minutes)it takes to commute to school for six days.Those results are: 25,22,17,20,15,and 10.Assuming the population is normally distributed,develop a 90% confidence interval for the population mean.
Determine the reliability factor from the Student's t distribution table.

A)1.476
B)2.015
C)3.365
D)4.032

Question 38

The upper limit of 90% confidence interval for the population proportion P,given a sample size n = 300 and sample proportion = 0.1833 is equal to:

A)0.1466
B)0.1395
C)0.2271
D)0.2200

Question 39

The 95% confidence interval for the population proportion P given a sample size n = 300 and sample proportion = 0.2933 is calculated as:

A)0.2933 ± 0.0515
B)0.2933 ± 0.0289
C)0.2933 ± 0.9200
D)0.2933 ± 0.8145

Question 40

Interval estimates for the variance of a normal population rely on the random variable (n - 1)s² / σ²,which follows:

A)a normal distribution.
B)a binomial distribution.
C)the Poisson distribution.
D)a chi-square distribution.

Question 41

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

A)77.530
B)72.231
C)74.727
D)79.273

Question 42

A sample of 50 students is taken from Utah Valley University (UVU).These students spent an average of $175 on books this semester,with a standard deviation of $25.A 95% confidence interval for the average amount of money spent on books for all students at UVU is equal to ________.(Hint: Use Excel function to obtain the critical value. )

A)175 ± 3.47
B)175 ± 7.18
C)175 ± 7.51
D)175 ± 3.86

Question 43

The bias of an estimator
is equal to E(
)- θ.

Question 44

If the population is normally distributed,both the sample mean and the median are unbiased estimators of the population mean.

Question 45

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let X₁,X₂,X₃,and X₄ be a random sample of observations from a population with mean μ and variance σ².Consider the following two point estimators of μ:
₁ = 0.10 X₁ + 0.40 X₂ + 0.40 X₃ + 0.10 X₄ and
₂ = 0.20 X₁ + 0.30 X₂ + 0.30 X₃ + 0.20 X₄
Which of the following statements is true?

A)
₁ is biased,but

₂ is an unbiased estimator of μ.
B)
₁ is unbiased,but

₂ is a biased estimator of μ.
C)Both
₁ and

₂ are unbiased estimators of μ.
D)Both
₁ and

₂ are biased estimators of μ.

Question 46

All other things being equal,the larger the sample size,the narrower the interval estimates that reflect the uncertainty about a parameter's true value.

Question 47

Consider the following random sample from a normal population: 14,10,13,16,12,18,15,and 11.What is the 95% confidence interval for the population variance?

A)11.39 to 15.86
B)3.11 to 29.51
C)6.54 to 38.82
D)1.12 to 5.69

Question 48

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let X₁,X₂,X₃,and X₄ be a random sample of observations from a population with mean μ and variance σ².Consider the following two point estimators of μ:
₁ = 0.10 X₁ + 0.40 X₂ + 0.40 X₃ + 0.10 X₄ and
₂ = 0.20 X₁ + 0.30 X₂ + 0.30 X₃ + 0.20 X₄
What is the relative efficiency of ₁ with respect to
₂?

A)1.05
B)0.98
C)1.30
D)0.76

Question 49

When computing the confidence interval for the population proportion,the Student's t-distribution is used rather than the normal distribution.

Question 50

A sample statistic such that the mean of all its possible values equals the population parameter the statistic seeks to estimate is an unbiased estimator.

Question 51

If a sample of size 21 is selected,the value of A for the probability P(t ≥A)= 0.025 is:

A)2.528
B)2.086
C)2.518
D)2.080

Question 52

The point estimator
is said to be an unbiased estimator of θ if Var(
)= Var(θ).

Question 53

If a sample of size 61 is selected,the value of A for the probability P(-A ≤ t ≤A)= 0.95 is:

A)2.000
B)2.021
C)1.677
D)1.671

Question 54

If a sample of size 41 is selected,the value of A for the probability P(-A ≤ t ≤A)= 0.90 is:

A)1.303
B)1.684
C)2.021
D)2.423

Question 55

The following sample was taken from a normally distributed population: 20,27,15,20,16,22,and 13.A 95% confidence interval for the population mean using this sample is:

A)19 ± 5.603
B)19 ± 2.201
C)19 ± 8.804
D)19 ± 4.402

Question 56

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let X₁,X₂,X₃,and X₄ be a random sample of observations from a population with mean μ and variance σ².Consider the following two point estimators of μ:
₁ = 0.10 X₁ + 0.40 X₂ + 0.40 X₃ + 0.10 X₄ and
₂ = 0.20 X₁ + 0.30 X₂ + 0.30 X₃ + 0.20 X₄
Which of the following constraints is true?

A)Var( ₁)= Var(
B)Var( ₂)₁)> Var( ₂)
C)Var( ₁)< Var( ₂)
D) = 0.76

Question 57

In order to estimate the average daily down time,a manufacturer randomly sampled 41 days of production records and found a mean of 51.75 minutes and standard deviation of 7.9 minutes.A 90% confidence interval for the population mean is:

A)51.75 ± 4.76
B)51.75 ± 3.28
C)51.75 ± 2.08
D)51.75 ± 1.30

Question 58

The lower limit of the 90% confidence interval for the population proportion P,given that n = 400;and
= 0.10 is 0.1247.

Question 59

If Var ( ₁)= σ² and Var ( ₂)= 2σ²,then the relative efficiency of
₁ with respect to
₂ is equal to 0.5.

Question 60

If a sample of size 120 is selected,the value of A for the probability P(-A ≤ t ≤A)= 0.98 is:

A)1.960
B)2.576
C)1.282
D)2.326

Question 61

The margin of error can be reduced by decreasing the sample size.

Question 62

The quantity 100 (1 + α)% is called the confidence level of the interval.

Question 63

An unbiased estimator of a population parameter is an estimator whose variance is the same as the actual value of the population variance.

Question 64

The probability density functions of normal distributions and t distributions are symmetric about their means.

Question 65

A point estimate is an estimate of a population parameter expressed as a single numerical value.

Question 66

As the confidence level for a confidence interval increases,the width of the interval also increases.

Question 67

The Student's t distribution is the ratio of the standard normal distribution to the square root of the chi-square distribution divided by its degrees of freedom.

Question 68

The width of a confidence interval is equal to twice the margin of error.

Question 69

The larger the sampling error,the smaller the sample size needed to develop the confidence interval.

Question 70

The process of inferring the values of unknown population parameters from those of known sample statistics is called estimation.

Question 71

For a 90% confidence interval,the reliability factor is equal to 1.96.

Question 72

Like the standard normal distribution,all t - distributions have a mean of zero and a standard deviation of 1.

Question 73

An interval estimate is an interval that provides an upper and lower bound for a specific population parameter whose value is unknown.

Question 74

Keeping all other factors constant,the more the population standard deviation is reduced,the smaller the margin of error.

Question 75

Confidence intervals for the population proportion are centered on the sample proportion.

Question 76

The sample standard deviation s is an unbiased estimator of the population standard deviation σ.

Question 77

The t-distribution with n -1 degrees of freedom is often used to construct confidence intervals of the population mean when the population standard deviation is known.

Question 78

An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated.

Question 79

If the shopping times for a random sample of 25 shoppers in a supermarket are normally distributed with a known population standard deviation of 15 minutes,the standard error is equal to 0.6.

Question 80

The density function of the standard normal distribution has a wider dispersion than the Student's t distribution.