ST260 Exam 4

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is a- .0495 b- 0 c- .4505 d- .9505

A

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 98% confidence interval for the true average age of all students in the university is a. 24.4 to 25.6. b. 20.0 to 30.0. c. 20.5 to 29.5. d. 23.0 to 27.0.

A

A sample of 92 observations is taken from an infinite population. The sampling distribution of x̄ is approximately a- normal because of the central limit theorem. b- normal because x̄ is always approximately normally distributed. c- normal because the sample size is small in comparison to the population size. d- None of these alternatives are correct.

A

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. t distribution with 24 degrees of freedom. b. t distribution with 25 degrees of freedom. c. t distribution with 26 degrees of freedom. d. normal distribution

A

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is a. 3.92. b. 15. c. 2.0. d. 4.

A

In general, higher confidence levels provide a. wider confidence intervals. b. a smaller standard error. c. unbiased estimates. d. narrower confidence intervals

A

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. At 95% confidence, the size of the margin of error is a. 98.00. b. 1.96. c. 50.00. d. 42.00.

A

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. The standard error of the mean is a- 50 b- 500 c- 81 d- 450

A

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 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. The standard error of the mean is a- .20 b- 7.50 c- 2.00 d- .39

A

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 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. 2.804 to 3.196. b. 1.36 to 4.64. c. 1 to 5. d. 2.5 to 3.5

A

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 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. .196. b. .10. c. 1.96. d. 1.64.

A

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 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- .100 b- .001 c- 1.000 d. .010

A

The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is a. 117. b. 10. c. 116. d. 11.

A

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the a. degrees of freedom. b. finite correction factor. c. sample size. d. standard deviation

A

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. margin of error. b. parameter estimate. c. confidence level. d. planning value

A

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. 2n. c. n. d. n + 1.

A

When s is used to estimate σ, the margin of error is computed by using the a. t distribution. b. normal distribution. c. mean of the sample. d. mean of the population

A

Whenever the population has a normal probability distribution, the sampling distribution of x bar is a normal probability distribution for a- any sample size b- samples of size thirty or greater c- small sample sizes d- large sample sizes

A

a simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained: 12 18 19 20 21 a point estimate of the mean is a- 18 b- 20 c- 400 d- 10

A

as sample size increases, the variability among the sample means a- decreases b- increases c- depends upon the specific population being sampled d- remains the same

A

parameters are a- numerical characteristics of a population b- the averages taken from a sample c- numerical characteristics of a sample d- numerical characteristics of either a sample or a population

A

sampling distribution of x bar is the a- probability distribution of the sample mean b- mean of the population c- probability distribution of the sample proportion d- mean of the sample

A

the following data was collected from a simple random sample of a population: 13 15 14 16 12 the mean of the population a- could be any value b- is 15.1581 c- is 15 d- is 14

A

the following data was collected from a simple random sample of a population: 13 15 14 16 12 the point estimate of the population mean a- is 14 b- cannot be determined, since the population size is unknown c- is 4 d- is 5

A

the following information was collected from a simple random sample of a population: 16 19 18 17 20 18 the point estimate of the mean of the population is a- 18 b- 108 c- 19.6 d- 16

A

the purpose of statistical inference is to provide information about the a- population based upon information contained in the sample b- population based upon information contained in the population c- sample based upon information contained in the population d- mean of the sample based upon the mean of the population

A

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the sample mean will be between 183 and 186 is a- 0.3413 b- 0.1359 c- 0.8185 d- 0.4772

B

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is a- 0.5228 b- 0.0228 c- 0.9772 d- .4772

B

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is a- 8.3600 b- 0.9511 c- 0.7200 d- 0.0347

B

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is a. 8.3. b. 9.8. c. 8.225. d. 9.92.

B

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The value of the margin of error at 95% confidence is a. 7.00. b. 1.61. c. .81. d. 80.83

B

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The standard error of the mean is a- 80.83 b- .8083 c- 7.0 d- 1.611

B

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12 respectively. The standard error of the mean is a- 0.12 b- 1.20 c- 8.00 d- 0.80

B

A simple random sample of 144 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is a- 1234 +- 120 b- 10 c- 1440 d- 120

B

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

B

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is the a. t distribution with n - 1 degrees of freedom. b. normal distribution. c. t distribution with n + 1 degrees of freedom. d. t distribution with n degrees of freedom.

B

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be a. 1.96. b. .95. c. .485. d. 1.645

B

In developing an interval estimate, if the population standard deviation is unknown a. the standard deviation is arrived at using the range. b. the sample standard deviation must be used. c. it is assumed that the population standard deviation is 1. d. it is impossible to develop the interval estimate.

B

In interval estimation, as the sample size becomes larger, the interval estimate a. becomes wider. b. becomes narrower. c. gets closer to 1.96. d. remains the same, because the mean is not changing.

B

In interval estimation, the t distribution is applicable only when a. the variance of the population is known. b. the sample standard deviation is used to estimate the population standard deviation. c. the mean of the population is unknown. d. the population has a mean of less than 30

B

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is a. 1776 to 1940 kWh. b. 1760 to 1956 kWh. c. 1758 to 1958 kWh. d. 1729 to 1987 kWh.

B

It is known that the population variance (σ ) is 144. At 95% confidence, what sample size should be taken so that the margin of error does not exceed 5? a. 24 b. 23 c. 25 d. 22

B

The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____. a. population proportion, standard error b. point estimate, margin of error c. population mean, standard error d. planning value, confidence coefficient

B

The level of significance α a. can be any positive value. b. is (1 - confidence coefficient). c. can be any value between -1.96 to 1.96. d. is always a negative value.

B

a subset of a population selected to represent the population is a- a parameter b- a sample c- small population d- a subset

B

as sample size increases, the a- a standard error of the mean increases b- a standard error of the mean decreases c- standard deviation of the population decreases d- population mean increases

B

as the sample size becomes larger, the sampling distribution of the sample mean approaches a a- binomial distribution b- normal distribution c- poisson distribution d- chi-square distribution

B

the fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large based on the a- assumption that the population has a normal distribution b- central limit theorem c- fact that we have tables of areas for the normal distribution d- none of these alternatives are correct

B

the sample statistic of s is the point estimator of a- x bar b- o c- u d- p

B

the sampling distribution of the sample mean a- is an unbiased estimator b- is the probability distribution showing all possible values of the sample mean c- is used as a point estimator of the population mean of u d- shows the distribution of all possible values of u

B

the standard deviation of a point estimator is called the a- standard deviation b- standard error c- point estimator d- variance of estimation

B

which of the following is(are) point estimator(s)? a- u b- s c- a d-o

B

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. 62. b. 60. c. 63. d. 61

C

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. 80. b. 50.07. c. 59.94. d. 1.998.

C

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 t value needed to develop the 95% confidence interval for the population mean SAT score is a. 1.96. b. 1.645. c. 1.998. d. 1.28.

C

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. t distribution with 199 degrees of freedom. b. t distribution with 201 degrees of freedom. c. normal distribution. d. t distribution with 200 degrees of freedom.

C

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. If we want to determine a 95% confidence interval for the average hourly income of the population, the value of t is a. 1.645. b. 1.96. c. 1.993. d. 1.28.

C

As the degrees of freedom increase, the t distribution approaches the a. uniform distribution. b. p distribution. c. normal distribution. d. exponential distribution

C

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. fluctuates. c. becomes smaller. d. stays the same

C

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 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. If the sample mean is 9 hours, then the 95% confidence interval is a. 7.36 to 10.64 hours. b. 7.04 to 10.96 hours. c. 8.61 to 9.39 hours. d. 7.80 to 10.20 hours

C

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 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately a. 1.96. b. 1.64. c. .39. d. .20

C

The degrees of freedom associated with a t distribution are a function of the a. area in the upper tail. b. confidence coefficient. c. sample size. d. sample standard deviation

C

The t value for a 95% confidence interval estimation with 24 degrees of freedom is a. 2.069. b. 2.492. c. 2.064. d. 1.711.

C

To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except a. confidence level. b. population standard deviation. c. degrees of freedom. d. desired margin of error

C

a probability distribution of all possible values of a sample statistic is known as a a- a parameter b- simple random sampling c- a sampling distribution d- a sample statistic

C

for a population with any distribution, the form of the sampling distribution of the sample mean is a- sometimes normal for large sample sizes b- sometimes normal for all sample sizes c- always normal for large sample sizes d- always normal for all sample sizes

C

the basis for using a normal probability distribution is to approximate the sampling distribution of x bar is a- the empirical rule b- Bayes' theorem c- the central limit theorem d- chebyshev's theorem

C

the sample mean is the point estimator of a- o b- x c- u d- p

C

the sampling error is the a- standard deviation multiplied by the sample size b- error caused by selecting a bad sample c- difference between the value of the sample mean and the value of the population mean d- same as the standard error of the mean

C

the standard deviation of x bar is referred to as the a- standard mean of x b- sample standard mean c- standard error of the mean d- sample mean deviation

C

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is a- 0.4332 b- 0.9332 c- 0.0668 d- 0.9544

D

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. 77.40 to 86.60. b. 80.48 to 87.52. c. 68.00 to 100.00. d. 82.99 to 85.01

D

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. 1349.93 to 1450.07. b. 1341.20 to 1458.80. c. 1320.32 to 1479.68. d. 1340.06 to 1459.94.

D

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is a. 171.78 to 188.22. b. 105 to 225. c. 175 to 185. d. 170.2 to 189.8

D

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of x̄ is a- approximately normal because the sample size is large in comparison to the population size. b- approximately normal because x̄ is always approximately normally distributed. c- approximately normal because of the central limit theorem. d- normal if the population is normally distributed

D

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The 95% confidence interval for the average hourly wage (in $) of all information system managers is a. 37.54 to 43.96. b. 39.40 to 42.10. c. 38.61 to 42.89. d. 39.14 to 42.36

D

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is a- 40 b- 1.875 c- 5 d- 15

D

From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is a- 3 b- greater than 2 c- 2 d- less than 2

D

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately a- 1.1022 b- 30 c- 2 d- 1.4847

D

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 sample size must be increased in order to develop an interval estimate. c. The t distribution with 50 degrees of freedom must be used. d. The t distribution with 49 degrees of freedom must be used

D

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the a. sample size to increase. b. width of the confidence interval to decrease. c. width of the confidence interval to remain the same. d. width of the confidence interval to increase.

D

In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 61 items is selected. The mean of the sample is determined to be 23. The associated number of degrees of freedom for reading the t value is a. 23. b. 22. c. 61. d. 60

D

It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is a. 189. b. 190. c. 74. d. 75.

D

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample mean for this situation? a- Approximately normal because of the central limit theorem b- Exactly normal c- Approximately normal because the sample size is small relative to the population size d- None of these alternatives are correct

D

The ability of an interval estimate to contain the value of the population parameter is described by the a. degrees of freedom. b. precise value of the population mean μ. c. point estimate. d. confidence level.

D

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. confidence coefficient. b. margin of error. c. proportion estimate. d. same as α.

D

The t distribution should be used whenever a. the population is not normally distributed. b. the sample size is less than 30. c. the population standard deviation is known. d. the sample standard deviation is used to estimate the population standard deviation.

D

a single numerical value used as an estimate of a population parameter is known as a a- a parameter b- a population parameter c- a mean estimator d- a point estimate

D

if we consider the simple random sampling process as an experiment, the sample mean is a- always zero b- always smaller than population mean c- exactly equal to the population mean d- a random variable

D

the sample statistic, such as x bar, s, or p bar, that provides the point estimate of the population parameter is known as a- a parameter b- population parameter c- population statistic d- a point estimator

D

in point estimation, a- data from the population is used to estimate the population parameter b- the mean of the population equals the mean of the sample c- data from the sample is used to estimate the sample statistic d- data from the sample is used to estimate the population parameter

dD