ST 260 Final
Parameters are a. numerical characteristics of a sample b. numerical characteristics of a population c. the averages taken from a sample d. numerical characteristics of either a sample or a population
B
The absolute value of the difference between the point estimate and the population parameter it estimates is a. the standard error b. the sampling error c. precision d. the error of confidence
B
The closer the sample mean is to the population mean, a. the larger the sampling error b. the smaller the sampling error c. the sampling error equals 1 d. None of these alternatives is correct.
B
The level of significance is the a. maximum allowable probability of Type II error b. maximum allowable probability of Type I error c. same as the confidence coefficient d. same as the p-value
B
The probability distribution of all possible values of the sample mean x̅is a. the probability density function of x̅ b. the sampling distribution of x̅ c. the grand mean, since it considers all possible values of the sample mean d. one, since it considers all possible values of the sample mean
B
The probability distribution of the sample mean is called the a. central probability distribution b. sampling distribution of the mean c. random variation d. standard error
B
The probability of making a Type II error is denoted by a. α b. β c. 1 - α d. 1 - β
B
The purpose of statistical inference is to provide information about the a. sample based upon information contained in the population b. population based upon information contained in the sample c. population based upon information contained in the population d. mean of the sample based upon the mean of the population
B
The sample statistic s is the point estimator of a. μ b. σ c. x̅ d. p̅
B
The sampling error is the a. same as the standard error of the mean b. difference between the value of the sample mean and the value of the population mean c. error caused by selecting a bad sample d. standard deviation multiplied by the sample size
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
The standard deviation of all possible x̅values is called the a. standard error of proportion b. standard error of the mean c. mean deviation d. central variation
B
The value added 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. interval estimate
B
Using an α = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion a. becomes narrower b. becomes wider c. does not change d. remains the same
B
When s is used to estimate σ, the margin of error is computed by using a. normal distribution b. t distribution c. the mean of the sample d. the mean of the population
B
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 size
B
The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the a. central limit theorem b. fact that we have tables of areas for the normal distribution c. assumption that the population has a normal distribution d. None of these alternatives is correct.
A
The p-value is a probability that measures the support (or lack of support) for the a. null hypothesis b. alternative hypothesis c. either the null or the alternative hypothesis d. sample statistic
A
The probability of making a Type I error is denoted by a. α b. β c. 1 - α d. 1 - β
A
The sample mean is the point estimator of a. μ b. σ c. x̅ d. p̅
A
The sample statistic, such as x̅, s, or p̅, that provides the point estimate of the population parameter is known as a. a point estimator b. a parameter c. a population parameter d. a population statistic
A
The sampling distribution of the sample means a. is the probability distribution showing all possible values of the sample mean b. is used as a point estimator of the population mean μ c. is an unbiased estimator d. shows the distribution of all possible values of μ
A
Sampling distribution of x̅is the a. probability distribution of the sample mean b. probability distribution of the sample proportion c. mean of the sample d. mean of the population
A
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. degrees of freedom minus 1
A
The error of rejecting a true null hypothesis is a. a Type I error b. a Type II error c. is the same as β d. committed when not enough information is available
A
What type of error occurs if you fail to reject H0 when, in fact, it is not true? a. Type II b. Type I c. either Type I or Type II, depending on the level of significance d. either Type I or Type II, depending on whether the test is one tail or two tail
A
When the following hypotheses are being tested at a level of significance of α H0: μ ≥ 500 Ha: μ < 500 the null hypothesis will be rejected if the p-value is a. ≤ α b. > α c. > α/2 d. ≤ 1 - α/2
A
When the p-value is used for hypothesis testing, the null hypothesis is rejected if a. p-value ≤ α b. α < p-value c. p-value ≥ α d. p-value = 1 - α
A
The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is a. H0: μ < 5 Ha : μ ≤ 5 b. H0: μ ≤ 5 Ha: μ > 5 c. H0: μ > 5 Ha: μ ≤ 5 d. H0: μ ≥ 5 Ha : μ < 5
B
Stratified random sampling is a method of selecting a sample in which a. the sample is first divided into strata, and then random samples are taken from each stratum b. various strata are selected from the sample c. the population is first divided into strata, and then random samples are drawn from each stratum d. None of these alternatives is correct.
C
The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is a. H0: P > 0.35 Ha: P ≥ 0.35 b. H0: P ≤ 0.35 Ha: P > 0.35 c. H0: P ≥ 0.35 Ha: P < 0.35 d. H0: P > 0.35 Ha: P ≤ 0.35
C
The level of significance a. can be any positive value b. can be any value c. is (1 - confidence level) d. can be any value between -1.96 to 1.96
C
The level of significance in hypothesis testing is the probability of a. accepting a true null hypothesis b. accepting a false null hypothesis c. rejecting a true null hypothesis d. None of these alternatives is correct.
C
The p-value ranges between a. zero and infinity b. minus infinity to plus infinity c. zero to one d. -1 to +1
C
The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is a. H0: P < 0.30 Ha : P ≥ 0.30 b. H0: P ≤ 0.30 Ha : P > 0.30 c. H0: P ≥ 0.30 Ha : P < 0.30 d. H0: P > 0.30 Ha : P ≤ 0.30
C
Whenever the population has a normal probability distribution, the sampling distribution of x̅is a normal probability distribution for a. only large sample sizes b. only small sample sizes c. any sample size d. only samples of size thirty or greater
C
Whenever using the t distribution for interval estimation (when the sample size is very small), we must assume that a. the sample has a mean of at least 30 b. the sampling distribution is not normal c. the population is approximately normal d. the finite population correction factor is necessary
C
Which of the following does not need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. None of these alternatives is correct.
C
Which of the following is (are) point estimator(s)? a. σ b. μ c. s d. α
C
A probability distribution for all possible values of a sample statistic is known as a. a sample statistic b. a parameter c. simple random sampling d. a sampling distribution
D
A sample of 20 items from a population with an unknown σ is selected in order to develop an interval estimate of μ. Which of the following is not necessary? a. We must assume the population has a normal distribution. b. We must use a t distribution. c. Sample standard deviation must be used to estimate σ. d. The sample must have a normal distribution.
D
A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of x̅is a. approximately normal because x̅is always approximately normally distributed b. approximately normal because the sample size is large in comparison to the population size c. approximately normal because of the central limit theorem d. normal if the population is normally distributed
D
A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a a. population parameter b. biased estimate of the population mean c. sample parameter d. point estimate
D
A single numerical value used as an estimate of a population parameter is known as a. a parameter b. a population parameter c. a mean estimator d. a point estimate
D
A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is a. H0: μ < 12 Ha: μ ≤ 12 b. H0: μ ≤ 12 Ha: μ > 12 c. H0: μ ≠ 12 Ha: μ = 12 d. H0: μ = 12 Ha: μ ≠ 12
D
An interval estimate is a range of values used to estimate a. the shape of the population's distribution b. the sampling distribution c. a sample statistic d. a population parameter
D
For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis a. could be rejected or not rejected depending on the sample size b. could be rejected or not rejected depending on the value of the mean of the sample c. is not rejected d. is rejected
D
For a population with any distribution, the form of the sampling distribution of the sample mean is a. sometimes normal for all sample sizes b. sometimes normal for large sample sizes c. always normal for all sample sizes d. always normal for large sample sizes
D
In the hypothesis testing procedure, α is a. the level of significance b. the critical value c. the confidence level d. 1 - level of significance
A
A Type II error is committed when a. a true alternative hypothesis is mistakenly rejected b. a true null hypothesis is mistakenly rejected c. the sample size has been too small d. not enough information has been available
A
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 202 degrees of freedom
A
A sample statistic, such as a sample mean, is known as a. a statistic b. a parameter c. the mean deviation d. the central limit theorem
A
A simple random sample from an infinite population is a sample selected such that a. each element is selected independently and from the same population b. each element has a 0.5 probability of being selected c. each element has a probability of at least 0.5 of being selected d. the probability of being selected changes
A
A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have a. the same probability of being selected b. a probability of 1/n of being selected c. a probability of 1/N of being selected d. a probability of N/n of being selected
A
An assumption made about the value of a population parameter is called a a. hypothesis b. conclusion c. confidence d. significance
A
As the test statistic becomes larger, the p-value a. gets smaller b. becomes larger c. stays the same, since the sample size has not been changed d. becomes negative
A
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic a. at least as small as that provided by the sample b. at least as large as that provided by the sample c. at least as small as that provided by the population d. at least as large as that provided by the population.
A
For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is a. the normal distribution b. the t distribution with n degrees of freedom c. the t distribution with n + 1 degrees of freedom d. the t distribution with n + 2 degrees of freedom
A
If a hypothesis is not rejected at the 5% level of significance, it a. will also not be rejected at the 1% level b. will always be rejected at the 1% level c. will sometimes be rejected at the 1% level d. None of these alternatives is correct.
A
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect a. the size of the confidence interval to increase b. the size of the confidence interval to decrease c. the size of the confidence interval to remain the same d. the sample size to increase
A
In general, higher confidence levels provide a. wider confidence intervals b. narrower confidence intervals c. a smaller standard error d. unbiased estimates
A
A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means a. whenever the population is infinite b. whenever the sample size is more than 5% of the population size c. whenever the sample size is less than 5% of the population size d. The correction factor is not necessary if the population has a normal distribution
B
A population characteristic, such as a population mean, is called a. a statistic b. a parameter c. a sample d. the mean deviation
B
A subset of a population selected to represent the population is a. a subset b. a sample c. a small population d. a parameter
B
A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken. The correct set of hypotheses is a. H0: μ ≥ 80 Ha : μ < 80 b. H0: μ ≤ 80 Ha : μ > 80 c. H0: μ ≠ 80 Ha : μ = 80 d. H0: μ < 80 Ha : μ > 80
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. parameter value d. population estimate
B
As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever a. np ≥ 5 b. n(1 - p) ≥ 5 and n ≥ 30 c. n ≥ 30 and (1 - p) = 0.5 d. None of these alternatives is correct.
B
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. None of these alternatives is correct.
B
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. becomes negative
B
As the sample size increases, the margin of error a. increases b. decreases c. stays the same d. increases or decreases depending on the size of the mean
B
As the sample size increases, the variability among the sample means a. increases b. decreases c. remains the same d. depends upon the specific population being sampled
B
Doubling the size of the sample will a. reduce the standard error of the mean to one-half its current value b. reduce the standard error of the mean to approximately 70% of its current value c. have no effect on the standard error of the mean d. double the standard error of the mean
B
For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as a. likely as that provided by the sample b. unlikely as that provided by the sample c. likely as that provided by the population d. unlikely as that provided by the population
B
If a hypothesis is rejected at 95% confidence, it a. will always be accepted at 90% confidence b. will always be rejected at 90% confidence c. will sometimes be rejected at 90% confidence d. None of these alternatives is correct.
B
In hypothesis testing if the null hypothesis is rejected, a. no conclusions can be drawn from the test b. the alternative hypothesis is true c. the data must have been accumulated incorrectly d. the sample size has been too small
B
In hypothesis testing, a. the smaller the Type I error, the smaller the Type II error will be b. the smaller the Type I error, the larger the Type II error will be c. Type II error will not be effected by Type I error d. the sum of Type I and Ttype II errors must equal to 1
B
In hypothesis testing, the tentative assumption about the population parameter is a. the alternative hypothesis b. the null hypothesis c. either the null or the alternative d. None of these alternatives is correct.
B
In interval estimation, the t distribution is applicable only when a. the population has a mean of less than 30 b. the sample standard deviation is used to estimate the population standard deviation c. the variance of the population is known d. the standard deviation of the population is known
B
In order to use the normal distribution for interval estimation of μ when σ is known and the sample is very small, the population a. must be very large b. must have a normal distribution c. can have any distribution d. must have a mean of at least 1
B
In point estimation a. data from the population is used to estimate the population parameter b. data from the sample is used to estimate the population parameter c. data from the sample is used to estimate the sample statistic d. the mean of the population equals the mean of the sample
B
A sample of 92 observations is taken from an infinite population. The sampling distribution of x̅ is approximately a. normal because x̅ is always approximately normally distributed b. normal because the sample size is small in comparison to the population size c. normal because of the central limit theorem d. None of these alternatives is correct.
C
A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is a. H0: μ < 85 Ha: μ ≥ 85 b. H0: μ ≤ 85 Ha: μ > 85 c. H0: μ ≥ 85 Ha: μ < 85 d. H0: μ > 85 Ha: μ ≤ 85
C
A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the a. approximation theorem b. normal probability theorem c. central limit theorem d. central normality theorem
C
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation? a. Increase the level of confidence for the interval. b. Decrease the sample size. c. Increase the sample size. d. Reduce the population variance.
C
As the sample size becomes larger, the sampling distribution of the sample mean approaches a a. binomial distribution b. Poisson distribution c. normal distribution d. chi-square distribution
C
As the sample size increases, the a. standard deviation of the population decreases b. population mean increases c. standard error of the mean decreases d. standard error of the mean increases
C
Cluster sampling is a. a nonprobability sampling method b. the same as convenience sampling c. a probability sampling method d. None of these alternatives is correct.
C
Convenience sampling is an example of a. probabilistic sampling b. stratified sampling c. nonprobabilistic sampling d. cluster sampling
C
If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error a. will also increase from .01 to .05 b. will not change c. will decrease d. will increase
C
If we consider the simple random sampling process as an experiment, the sample mean is a. always zero b. always smaller than the population mean c. a random variable d. exactly equal to the population mean
C
In developing an interval estimate, if the population standard deviation is unknown a. it is impossible to develop an interval estimate b. the standard deviation is arrived at using the range c. the sample standard deviation can be used d. it is assumed that the population standard deviation is 1
C
In hypotheses testing, a. the sum of Type I and Type II errors must add up to 1 b. Type II is always twice as large as Type I error c. the probability of Type I error is α d. the probability of Type II error is β
C
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.
D
If a hypothesis is rejected at the 5% level of significance, it a. will always be rejected at the 1% level b. will always be accepted at the 1% level c. will never be tested at the 1% level d. may be rejected or not rejected at the 1% level
D
If a hypothesis test leads to the rejection of the null hypothesis, a. a Type II error must have been committed b. a Type II error may have been committed c. a Type I error must have been committed d. a Type I error may have been committed
D
In determining the sample size necessary to estimate a population proportion, which of the following information is not needed? a. the maximum margin of error that can be tolerated b. the confidence level required c. a preliminary estimate of the true population proportion P d. the mean of the population
D
In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true, a. a Type I error has been committed b. a Type II error has been committed c. either a Type I or Type II error has been committed d. the correct decision has been made
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 the sample size is small relative to the population size b. approximately normal because of the central limit theorem c. exactly normal d. None of these alternatives is correct.
D
Since the sample size is always smaller than the size of the population, the sample mean a. must always be smaller than the population mean b. must be larger than the population mean c. must be equal to the population mean d. can be smaller, larger, or equal to the population mean
D
The expected value of the random variable x̅is a. the standard error b. the sample size c. the size of the population d. None of these alternatives is correct.
D
The p-value a. is the same as the Z statistic b. measures the number of standard deviations from the mean c. is a distance d. is a probability
D
The power curve provides the probability of a. correctly accepting the null hypothesis b. incorrectly accepting the null hypothesis c. correctly rejecting the alternative hypothesis d. correctly rejecting the null hypothesisThe power curve
D
The probability distribution of all possible values of the sample proportion p̅is the a. probability density function of p̅ b. sampling distribution of x̅ c. same as p̅, since it considers all possible values of the sample proportion d. sampling distribution of p̅
D
The probability of committing a Type I error when the null hypothesis is true is a. the confidence level b. β c. greater than 1 d. the Level of Significance
D
The sampling error is the a. same as the standard error of the mean b. difference between the value of the sample mean and the value of the sample proportion c. error caused by selecting a bad sample d. absolute value of the difference between the proportion of the population and proportion of the sample
D
The set of all elements of interest in a study is a. set notation b. a set of interest c. a sample d. a population
D
The sum of the values of α and β a. always add up to 1.0 b. always add up to 0.5 c. is the probability of Type II error d. none of these alternatives is correct
D
Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation? a. standard distribution b. z distribution c. alpha distribution d. t distribution
D
Which of the following best describes the form of the sampling distribution of the sample proportion? a. When standardized, it is exactly the standard normal distribution. b. When standardized, it is the t distribution. c. It is approximately normal as long as n ≥ 30. d. It is approximately normal as long as np ≥ 5 and n(1-p) ≥ 5.
D
Which of the following is an example of nonprobabilistic sampling? a. simple random sampling b. stratified simple random sampling c. cluster sampling d. judgment sampling
D
Which of the following sampling methods does not lead to probability samples? a. stratified sampling b. cluster sampling c. systematic sampling d. convenience sampling
D
Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is a. H0: μ < 10.0% Ha : μ ≥ 10.0% b. H0: μ ≤ 10.0% Ha : μ > 10.0% c. H0: μ > 10.0% Ha : μ ≤ 10.0% d. H0: μ ≥ 10.0% Ha : μ < 10.0%
D