Deck 8: Interval Estimation

Question 1

A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ

A) becomes narrower.
B) becomes wider.
C) does not change.
D) becomes 100.1 to 120.1.

Answer 1

becomes narrower.

Question 2

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

A) confidence level.
B) interval estimate.
C) margin of error.
D) point estimate.

Answer 2

interval estimate.

Question 3

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

A) becomes larger.
B) becomes smaller.
C) stays the same.
D) fluctuates.

Answer 3

becomes smaller.

Question 4

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the

A) normal distribution.
B) t distribution with 25 degrees of freedom.
C) t distribution with 26 degrees of freedom.
D) t distribution with 24 degrees of freedom.

Question 5

In an interval estimation for a proportion of a population, the value of z at 99.2% confidence is

A) 2.65.
B) 2.41.
C) 1.96.
D) 1.645.

Question 6

In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 58 items is selected. The mean of the sample is determined to be 36. The associated number of degrees of freedom for reading the t value is

A) 35.
B) 36.
C) 57.
D) 58.

Question 7

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is the

A) normal distribution.
B) t distribution with n degrees of freedom.
C) t distribution with n + 1 degrees of freedom.
D) t distribution with n - 1 degrees of freedom.

Question 8

The z value for a 97.8% confidence interval estimation is

A) 2.02.
B) 1.96.
C) 2.00.
D) 2.29.

Question 9

In interval estimation, the t distribution is applicable only when the

A) population has a mean of less than 30.
B) sample standard deviation is used to estimate the population standard deviation.
C) variance of the population is known.
D) mean of the population is unknown.

Question 10

In interval estimation, as the sample size becomes larger, the interval estimate

A) becomes narrower.
B) becomes wider.
C) remains the same, because the mean is not changing.
D) gets closer to 1.96.

Question 11

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).

A) The normal distribution can be used.
B) The t distribution with 5 degrees of freedom must be used.
C) The t distribution with 6 degrees of freedom must be used.
D) The sample size must be increased.

Question 12

A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the

A) normal distribution.
B) t distribution with 200 degrees of freedom.
C) t distribution with 201 degrees of freedom.
D) t distribution with 199 degrees of freedom.

Question 13

From a population with a variance of 484, a sample of 256 items is selected. At 95% confidence, the margin of error is

A) 16.
B) 1.375.
C) 2.695.
D) 22.

Question 14

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be

A) .485.
B) 1.96.
C) .95.
D) 1.645.

Question 15

The t value for a 95% confidence interval estimation with 96 degrees of freedom is

A) 1.661.
B) 1.985.
C) 1.291.
D) 1.986.

Question 16

As the sample size increases, the margin of error

A) increases.
B) decreases.
C) stays the same.
D) fluctuates depending on the mean.

Question 17

In developing an interval estimate, if the population standard deviation is unknown,

A) it is impossible to develop the interval estimate.
B) the standard deviation is arrived at using the range.
C) the sample standard deviation must be used.
D) it is assumed that the population standard deviation is 1.

Question 18

When s is used to estimate σ, the margin of error is computed by using the

A) normal distribution.
B) t distribution.
C) mean of the sample.
D) mean of the population.

Question 19

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

A) confidence level.
B) margin of error.
C) parameter estimate.
D) planning value.

Question 20

A population has a standard deviation of 25. A random sample of 125 items from this population is selected. The sample mean is determined to be 325. At 95% confidence, the margin of error is

A) 2.24.
B) 5.
C) 4.38.
D) 11.18.

Question 21

A machine that produces a major part for an airplane engine is monitored closely. In the past, 6% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

A) 70.
B) 69.
C) 135.
D) 136.

Question 22

We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor. What is the minimum sample size needed to estimate the population proportion with a margin of error of .05 or less at 95% confidence?

A) 200.
B) 100.
C) 58.
D) 385.

Question 23

In a random sample of 144 observations, = .7. The 95% confidence interval for p is

A) .63 to .77.
B) .44 to .96.
C) .65 to .75.
D) .64 to .76.

Question 24

A random sample of 64 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is

A) 15.2 to 24.8.
B) 18.8 to 21.2.
C) 18.986 to 21.014.
D) 21.2 to 22.8.

Question 25

The ability of an interval estimate to contain the value of the population parameter is described by the

A) confidence level.
B) degrees of freedom.
C) precise value of the population mean μ.
D) point estimate.

Question 26

In general, higher confidence levels provide

A) wider confidence intervals.
B) narrower confidence intervals.
C) a smaller standard error.
D) unbiased estimates.

Question 27

A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is

A) 83.45 to 84.55.
B) 80.07 to 87.93.
C) 83.29 to 84.71.
D) 80.5 to 87.5.

Question 28

It is known that the population variance equals 529. With a .95 probability, the sample size that needs to be taken if the desired margin of error is 4 or less is

A) 508.
B) 127.
C) 509.
D) 128.

Question 29

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 98% confidence interval for μ is

A) 105 to 225.
B) 175 to 185.
C) 165.6 to 194.4.
D) 164.575 to 195.425.

Question 30

The sample size needed to provide a margin of error of 3 or less with a .95 probability when the population standard deviation equals 11 is

A) 10.
B) 11.
C) 51.
D) 52.

Question 31

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

A) .871 to .929.
B) .120 to .280.
C) .765 to .835.
D) .071 to .129.

Question 32

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion

A) becomes narrower.
B) becomes wider.
C) uses a zero margin of error.
D) remains the same.

Question 33

The following random sample from a population whose values were normally distributed was collected. 10
8
11
11
​
The 95% confidence interval for μ is

A) 8.52 to 11.48.
B) 7.75 to 12.25.
C) 9.25 to 10.75.
D) 8.00 to 10.00.

Question 34

A random sample of 1000 people was taken. Seven hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favor Candidate A is

A) .723 to .777.
B) .727 to .773.
C) .70 to .80.
D) .725 to .775.

Question 35

When the level of confidence decreases, the margin of error

A) stays the same.
B) becomes smaller.
C) becomes larger.
D) becomes smaller or larger, depending on the sample mean.

Question 36

In a random sample of 100 observations, = .2. The 95% confidence interval for p is

A) .1342 to .2658.
B) .15 to .25.
C) 0 to .4.
D) .1216 to .2784.

Question 37

The following random sample from a population whose values were normally distributed was collected. 10
12
18
16
​
The 80% confidence interval for μ is

A) 12.054 to 15.946.
B) 10.108 to 17.892.
C) 10.321 to 17.679.
D) 11.009 to 16.991.

Question 38

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 95% confidence interval for the true average age of all students in the university is

A) 24.6 to 25.4.
B) 24.5 to 25.5.
C) 23.0 to 27.0.
D) 20.0 to 30.0.

Question 39

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the

A) width of the confidence interval to increase.
B) width of the confidence interval to decrease.
C) width of the confidence interval to remain the same.
D) sample size to increase.

Question 40

When constructing a confidence interval for the population mean using the standard deviation of the sample, the degrees of freedom for the t distribution equals

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

Question 41

The manager of a grocery store has taken a random sample of 144 customers. The average length of time it took these 144 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The standard error of the mean equals

A) .008.
B) .833.
C) .083.
D) 1.000.

Question 42

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. If we want to provide a 95% confidence interval for the population mean SAT score, the degrees of freedom for reading the t value is

A) 60.
B) 61.
C) 62.
D) 63.

Question 43

In order to estimate the average electric usage per month, a sample of 64 houses was selected and the electric usage was determined. Assume a population standard deviation of 320 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is _____ kWh.

A) 1779.6 to 1936.4
B) 1818 to 1898
C) 1792.2 to 1923.8
D) 1538 to 2178

Question 44

A sample of 100 information systems managers had an average hourly income of $40.00 with a standard deviation of $8.00. If we want to determine a 95% confidence interval for the average hourly income of the population, the value of t is

A) 1.96.
B) 1.645.
C) 1.28.
D) 1.993.

Question 45

The manager of a grocery store has taken a random sample of 144 customers. The average length of time it took these 144 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. With a .95 probability, the sample mean will provide a margin of error of

A) 1.63.
B) .137.
C) .163.
D) 1.37.

Question 46

From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is selected to develop an interval estimate for µ. Which of the following statements is true?​

A) ​The standard normal distribution can be used.
B) ​The t distribution with 50 degrees of freedom must be used.
C) ​The t distribution with 49 degrees of freedom must be used.
D) ​The sample size must be increased in order to develop an interval estimate.

Question 47

In order to estimate the average electric usage per month, a sample of 64houses was selected and the electric usage was determined. Assume a population standard deviation of 320 kilowatt-hours. At 95% confidence, the size of the margin of error is

A) 1.96.
B) 40.00.
C) 78.40.
D) 65.80.

Question 48

A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?

A) ​95% of the sample of employees has a systolic blood pressure between 123 and 139.
B) ​If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
C) ​95% of the population of employees has a systolic blood pressure between 123 and 139.
D) ​If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.

Question 49

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when​

A) ​np > 5.
B) ​n(1 - p) > 5.
C) ​p has a normal distribution.
D) ​both np > 5 and n(1 - p) > 5.

Question 50

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 64 business students over a one-week period. Assume the population standard deviation is 1.6 hours. The standard error of the mean is

A) 1.6.
B) .025.
C) 2.00.
D) .20.

Question 51

A sample of 100 information systems managers had an average hourly income of $40.00 with a standard deviation of $8.00. The value of the margin of error at 95% confidence is

A) 80.
B) 8.
C) .10.
D) 1.568.

Question 52

A sample of 100 information systems managers had an average hourly income of $40.00 with a standard deviation of $8.00. The standard error of the mean is

A) 80.
B) .8.
C) 8.
D) .08.

Question 53

A random sample of 81 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 300. The t value needed to develop the 95% confidence interval for the population mean SAT score is

A) 1.96.
B) 1.998.
C) 1.645.
D) 1.28.

Question 54

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. The margin of error at 95% confidence is

A) 1.998.
B) 50.07.
C) 80.
D) 59.94.

Question 55

In order to estimate the average electric usage per month, a sample of 64 houses was selected and the electric usage was determined. Assume a population standard deviation of 320 kilowatt-hours. The standard error of the mean is

A) 320.
B) 64.
C) 400.
D) 40.

Question 56

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 64 business students over a one-week period. Assume the population standard deviation is 1.6 hours. With a .95 probability, the margin of error is approximately

A) .392.
B) 1.96.
C) .20.
D) 1.645.

Question 57

The manager of a grocery store has taken a random sample of 144 customers. The average length of time it took these 144 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The 95% confidence interval for the true average checkout time (in minutes) is

A) 2.863 to 3.137.
B) 1.36 to 4.64.
C) 1 to 5.
D) 2.837 to 3.163.

Question 58

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. The 95% confidence interval for the population mean SAT score is

A) 1340.06 to 1459.94.
B) 1341.20 to 1458.80.
C) 1349.93 to 1450.07.
D) 1320.32 to 1479.68.

Question 59

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 64 business students over a one-week period. Assume the population standard deviation is 1.6 hours. If the sample mean is 9 hours, then the 95% confidence interval is _____ hours.

A) 7.04 to 10.96
B) 7.36 to 10.64
C) 7.80 to 10.20
D) 8.608 to 9.392

Question 60

A sample of 100 information systems managers had an average hourly income of $40.00 with a standard deviation of $8.00. The 95% confidence interval for the average hourly wage (in $) of all information system managers is

A) 38.684 to 41.316.
B) 32 to 48.
C) 38.432 to 41.568.
D) 39 to 41.

Question 61

We are interested in conducting a study in order to determine the percentage of voters in a city who would vote for the incumbent mayor. What is the minimum sample size needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?

A) 625
B) 626
C) 600
D) 601

Question 62

We can reduce the margin of error in an interval estimate of p by doing any of the following except​

A) ​increasing the sample size.
B) ​increasing the planning value p* to .5.
C) ​increasing α.
D) ​reducing the confidence coefficient.

Question 63

​The margin of error in an interval estimate of the population mean is a function of all of the following except

A) α.
B) ​sample mean.
C) ​sample size.
D) ​variability of the population.

Question 64

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except​

A) ​use the sample proportion from a previous study.
B) ​use the sample proportion from a preliminary sample.
C) ​use 1.0 as an estimate.
D) ​use judgment or a best guess.

Question 65

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

A) uniform
B) normal
C) exponential
D) p

Question 66

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the​

A) ​finite correction factor.
B) ​sample size.
C) ​degrees of freedom.
D) ​standard deviation.

Question 67

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except​

A) ​use the estimated σ from a previous study.
B) ​use the sample standard deviation from a preliminary sample.
C) ​use judgment or a best guess.
D) use .5 as an estimate.

Question 68

The mean of the t distribution is​

A) ​0.
B) ​.5.
C) ​1.
D) ​problem specific.

Question 69

The level of significance α

A) can be any positive value.
B) is always a negative value.
C) is (1 - confidence coefficient).
D) can be any value between -1.96 to 1.96.

Question 70

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

A) ​varies from sample to sample of the same size.
B) ​is the same for all samples of the same size.
C) ​increases as the sample size increases.
D) ​is independent of sample size.

Question 71

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed​

A) ​.05.
B) ​5.
C) ​10.
D) ​30.

Question 72

The t distribution should be used whenever the

A) sample size is less than 30.
B) sample standard deviation is used to estimate the population standard deviation.
C) population is not normally distributed.
D) population standard deviation is known.

Question 73

A random sample of 100,000 credit sales in a department store showed an average sale of $87.25. From past data, it is known that the standard deviation of the population is $20.00. Determine the standard error of the mean.

A) .0632
B) .0002
C) 20.00
D) .0141

Question 74

​The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____.

A) ​population mean, standard error
B) population proportion, standard error
C) ​point estimate, margin of error
D) ​planning value, confidence coefficient

Question 75

The sample size that guarantees the estimate of a population proportion satisfying the margin of error requirement is computed using a planning value of p equal to​

A) ​.01.
B) ​.50.
C) ​.51.
D) ​.99.

Question 76

The degrees of freedom associated with a t distribution are a function of the​

A) ​area in the upper tail.
B) ​sample standard deviation.
C) ​confidence coefficient.
D) ​sample size.

Question 77

To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except

A) desired margin of error.
B) confidence level.
C) population standard deviation.
D) degrees of freedom.

Question 78

Confidence intervals for the population mean µ and population proportion p _____ as the size of the sample increases.

A) become narrower
B) become wider
C) remain the same
D) get closer to 1.

Question 79

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the​

A) proportion estimate.
B) ​margin of error.
C) ​confidence coefficient.
D) same as α.

Question 80

It is known that the population variance (σ²) is 125. At 95% confidence, what sample size should be taken so that the margin of error does not exceed 3?

A) 52
B) 53
C) 54
D) 55