Deck 6: Sampling and Estimation

Question 1

The means of all possible samples of a fixed size n from some population will form a distribution which is known as the ________.

A)corollary of the mean
B)sampling distribution of the mean
C)standard error of the mean
D)point estimate

Answer 1

B

Question 2

________ is based on dividing a population into subgroups, sampling a set of subgroups, and conducting a complete census within the subgroups sampled.

A)Cluster sampling
B)Continuous process sampling
C)Judgment sampling
D)Systematic sampling

Answer 2

A

Question 3

From the standard deviation formula, s² ⁼ , identify the estimator.

Answer 3

A

Question 4

Which of the following is true of an unbiased estimator value?

A)The expected value will align perfectly with the population mean.
B)The expected value will not equal the population's parameters.
C)The expected value will not be greater than zero.
D)The expected value will equal the population's parameters.

Question 5

________ involves selecting items from a population so that every subset of a given size has an equal chance of being selected.

A)Convenience sampling
B)Subjective sampling
C)Judgment sampling
D)Simple random sampling

Question 6

Which of the following accurately describes a sampling distribution of the mean?

A)It is the mean of any one sample from a group of related populations of different sizes.
B)It is the mean of any one sample from a group of samples of varying sizes from a population.
C)It is the mean of half the samples from a related group of populations.
D)It is the means of all possible samples of a fixed size n from a group of population.

Question 7

Which of the following sampling methods bases its selection of samples on the ease of data collection?

A)probabilistic sampling
B)judgment sampling
C)simple random sampling
D)convenience sampling

Question 8

The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9.Which of the following is the answer for the probability that the next individual who buys a product will make a purchase of more than $116?

A)71%
B)48%
C)33%
D)42%

Question 9

In sampling, ________ involves assessing the value of an unknown population parameter-such as a population mean, population proportion, or population variance-using sample data.

A)distribution
B)randomization
C)estimation
D)substitution

Question 10

For which of the following is the value of the estimator said to be biased?

A)if the expected value of the estimator does not equal the population parameter
B)if the expected value of the estimator equals the population parameter
C)only if the expected value of the estimator is zero
D)only if the expected value of the estimator goes below zero

Question 11

________ are statistical errors that are caused due to the sample not representing the target population adequately.

A)Parallax errors
B)Sampling errors
C)Nonsampling errors
D)Quantization errors

Question 12

A ________ is a description of the approach that is used to obtain samples from a population prior to any data collection activity.

A)population frame
B)sampling weight
C)sampling plan
D)probability interval

Question 13

A(n)________ is a single number derived from sample data that is used to estimate the value of a population parameter.

A)confidence interval
B)frequentist interference
C)interval estimate
D)point estimate

Question 14

________ sampling applies to populations that are divided into natural subsets and allocates the appropriate proportion of samples to each subset.

A)Systematic
B)Stratified
C)Cluster
D)Continuous process

Question 15

Which of the following types of sampling involves using random procedures to select a sample?

A)judgment sampling
B)probabilistic sampling
C)subjective sampling
D)convenience sampling

Question 16

Which of the following describes periodic sampling?

A)It is a sampling method based solely on expert opinion.
B)It is a sampling method based on selecting a time and then sampling the products after that time.
C)It is a sampling method based on selecting every nth item from a population.
D)It is a sampling method exclusively used for population that is divided into subsets.

Question 17

Which of the following is implied from the standard error of the mean formula?

A)that true means of populations can be found easier than those of samples
B)that standard deviation increases with increase in sample size
C)that larger sample sizes provide greater accuracy in estimating the true population mean
D)that the true mean of the population can only be calculated using smaller sample sizes

Question 18

Which of the following is true of judgment sampling?

A)It selects samples based on expert opinion.
B)It selects samples based on ease of data collection.
C)It selects samples based on random procedures.
D)It selects samples based on full representation of all subsets in a population.

Question 19

Which of the following is the inherent reason why sampling errors occur?

A)because samples represent the whole population
B)because samples are only a subset of the population
C)because samples never provide enough data to estimate standard deviation
D)because the means cannot be accurately estimated using samples

Question 20

Which of the following is the equation for calculating the standard error of the mean?

Question 21

Use the table below to answer the following question(s).
The historical data of Velvetta Inc., a healthcare products manufacturer, have shown that in a production process for filling bottles of shampoo, variance in the volume is constant; however, clogs in the filling machine often affect the average volume.The historical standard deviation is 5 milliliters.In filling 250-milliliter bottles, a sample of 20 found an average volume of 242 milliliters.

Based on the data in the table above, calculate the margin of error at 95% confidence interval.

A)1)84
B)2)19
C)2)51
D)1)96

Question 22

The ________ is a family of probability distributions with a shape similar to the standard normal distribution.

A)log-normal distribution
B)Gaussian q-distribution
C)frequentist interference
D)t-distribution

Question 23

In which of the following cases is a proportion of the observations of a sample used in estimating the confidence interval?

A)when the degrees of freedom are too large
B)when a true sampling distribution cannot be estimated
C)when the population standard deviation is known
D)when variables have only two possible outcomes

Question 24

The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9.If a soccer team of 11 players were to make the next batch of orders, what would be the standard error of the mean?

A)1)64
B)2)71
C)3)67
D)0)82

Question 25

The formula for a 100(1 - α)% confidence interval for the mean μ when the population standard deviation is unknown is ________.

Question 26

Use the table below to answer the following question(s).
The historical data of Velvetta Inc., a healthcare products manufacturer, have shown that in a production process for filling bottles of shampoo, variance in the volume is constant; however, clogs in the filling machine often affect the average volume.The historical standard deviation is 5 milliliters.In filling 250-milliliter bottles, a sample of 20 found an average volume of 242 milliliters.

From the table above, calculate the lower confidence interval estimate at a confidence level of 95%

A)239.49
B)240.16
C)239.81
D)240.04

Question 27

Which of the following is true of calculating confidence intervals for larger samples?

A)For larger samples, the t-distribution is indistinguishable from the standard normal distribution.
B)For larger samples, both the t-distribution and the standard normal distribution require standard deviation values to be calculated.
C)For larger samples, the degrees of freedom cannot be calculated accurately.
D)For larger samples, only z-values provide a true sampling distribution of the mean.

Question 28

Which of the following is a difference between the t-distribution and the standard normal distribution?

A)The t-distribution cannot be calculated without a known standard deviation, while the standard normal distributions can be.
B)The standard normal distribution's confidence levels are wider than those of the t-distribution.
C)The t-distribution has a larger variance than the standard normal distribution.
D)The standard normal distribution is dependent on parameters like degrees of freedom, while t-distribution is not.

Question 29

A 100(1-α)% confidence interval for the population mean μ based on a sample of size n with a sample mean and a known population standard deviation σ is given by ________.

Question 30

The central limit theorem states that if the population is normally distributed, then the ________.

A)mean of the population can be calculated without using samples
B)standard error of the mean will not vary from the population mean
C)sampling distribution of the mean will vary from sample to sample
D)sampling distribution of the mean will also be normal for any sample size

Question 31

Use the table below to answer the following question(s).
The historical data of Velvetta Inc., a healthcare products manufacturer, have shown that in a production process for filling bottles of shampoo, variance in the volume is constant; however, clogs in the filling machine often affect the average volume.The historical standard deviation is 5 milliliters.In filling 250-milliliter bottles, a sample of 20 found an average volume of 242 milliliters.

From the table above, calculate the value at a 95% confidence interval.

A)1)64
B)1)84
C)1)96
D)2)19

Question 32

Which of the following is a difference between interval estimates and point estimates?

A)Point estimates cannot be used to calculate statistical error, while interval estimate is used to calculate statistical error.
B)Point estimates provide only a single value for a sample, while interval estimates provide us a range of values.
C)Point estimates indicate the magnitude of potential error in the estimate, while interval estimates don't.
D)Point estimates on an average provide more information than interval estimates.

Question 33

Which of the following types of distributions use z-values to establish confidence intervals?

A)Gaussian q-distribution
B)t-distribution
C)log-normal distribution
D)standard normal distribution

Question 34

In the equation for calculating a confidence interval for a proportion, represent?

A)the mean for the sampling distribution of the proportion
B)the degree of freedom for the sampling distribution of the proportion
C)the standard error for the sampling distribution of the proportion
D)the estimator for sampling distribution of the proportion

Question 35

________ states that if the sample size is large enough, the sampling distribution of the mean is approximately normally distributed, regardless of the distribution of the population and that the mean of the sampling distribution will be the same as that of the population.

A)Chebyshev's theorem
B)Central limit theorem
C)Prime number theorem
D)Oppermann's conjecture

Question 36

For the formula for calculating the confidence level with known standard deviation, the value ________ represents the value of a standard normal random variable with a cumulative probability of 1 - α / 2.

Question 37

Which of the following is true of the t-distribution?

A)It has narrower confidence intervals than the standard normal distribution.
B)It's only used to calculate confidence intervals where there is no known population standard deviation.
C)It converges to the standard normal distribution as degrees of freedom increase.
D)It does not require parameters such as degrees of freedom.

Question 38

The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9.If a soccer team of 11 players were to make the next batch of orders, what is the probability that the mean purchase would exceed $116?

A)11%
B)3%
C)33%
D)7%

Question 39

Use the table below to answer the following question(s).
The historical data of Velvetta Inc., a healthcare products manufacturer, have shown that in a production process for filling bottles of shampoo, variance in the volume is constant; however, clogs in the filling machine often affect the average volume.The historical standard deviation is 5 milliliters.In filling 250-milliliter bottles, a sample of 20 found an average volume of 242 milliliters.

From the table above, determine the cumulative probability for z at a 95% confidence level.

A)0)975
B)0)950
C)1
D)0)987

Question 40

A ________ is a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true population parameter.

A)point estimate
B)frequentist interference
C)confidence interval
D)fiducial inference

Question 41

A confidence interval is a range of values between which the value of the population parameter is believed to be.

Question 42

Convenience sampling is an example of a probabilistic sampling method.

Question 43

Which of the following is true of prediction intervals?

A)It provides estimates for variables that can have only two possible outcomes.
B)It is associated with the distribution of a random variable.
C)It provides an interval estimate of a population parameter.
D)It is associated with the sampling distribution of a statistic.

Question 44

Explain selecting a sample using the continuous process sampling methods.

Question 45

Point estimates do not provide any indication of the magnitude of the potential error in the estimate.

Question 46

Give an account of biased and unbiased estimators in sampling methods.

Question 47

For any sample size, the true sampling distribution of the mean is the standard deviation.

Question 48

As the number of degrees of freedom increases, the t-distribution converges to the standard normal distribution.

Question 49

What is a confidence interval in sampling?

Question 50

Which of the following is true of the equation for computing the sample size required to achieve a desired confidence interval half-width for a proportion?

A)The sample size calculated will only be an approximation.
B)The standard deviation need not be calculated first in order to compute the sample size.
C)The value for π is always set at 1.
D)The value for π is never a constant.

Question 51

The simple random sampling method is the only statistical sampling method that does not include sampling errors.

Question 52

As the sample size increases, the width of the confidence interval decreases.

Question 53

A ________ is one that provides a range for anticipating the value of a new observation from the same population.

A)prediction interval
B)confidence interval
C)t-distribution
D)standard normal distribution

Question 54

Compare between the t-distribution and the standard normal distribution.

Question 55

A confidence interval is associated with the sampling distribution of a statistic.

Question 56

The table below shows the number of goals scored by the Huntington Soccer Club in their league for the past 12 years.Calculate the standard error of the mean of the data given that the variance of the data is 50.45

Question 57

The table below shows the weights of female individuals in Catherine's family.Calculate the sample variance in the weights, and the standard deviation.

Question 58

Compare between a prediction interval and a confidence interval.

Question 59

Estimators are the measures used to estimate population parameters.