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

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

Answer 2

A

Question 3

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%

Answer 3

D

Question 4

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 5

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 6

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 7

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

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

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

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 10

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 11

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 12

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 13

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 14

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 parameter.

Question 15

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 distribution 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 distribution of the means of all possible samples of fixed size n from a population.

Question 16

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 17

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 18

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 19

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 20

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

Question 21

Which of the following is true of the equation [n ? (z?/2)2 $\frac { \pi ( 1 - \pi ) } { E ^ { 2 } }$ ] 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 ? is always set at 1.
D) The most conservative estimate for ? is 0.5.

Question 22

Discuss the applications of confidence interval estimation
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 mean volume. The historical standard deviation is 5 milliliters. In filling 250-milliliter bottles, a sample of 20 found a meanvolume of 242 milliliters. $$\begin{array} { | l | l | } \hline \text { Velvetta Inc. Shamp o0 } & \\\text { Production } & \\\hline \text { Alpha Vahe } & 0.05 \\\hline \text { Standard Deviation } & 5 \\\hline \text { Sample Size } & 20 \\\hline \text { Sample Mean } & 242 \\\hline\end{array}$$

-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 23

Discuss the applications of confidence interval estimation
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 mean volume. The historical standard deviation is 5 milliliters. In filling 250-milliliter bottles, a sample of 20 found a meanvolume of 242 milliliters. $$\begin{array} { | l | l | } \hline \text { Velvetta Inc. Shamp o0 } & \\\text { Production } & \\\hline \text { Alpha Vahe } & 0.05 \\\hline \text { Standard Deviation } & 5 \\\hline \text { Sample Size } & 20 \\\hline \text { Sample Mean } & 242 \\\hline\end{array}$$

-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 24

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 25

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 26

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 27

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

A) It has narrower confidence intervals than the standard normal distribution.
B) It is 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 28

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 29

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 30

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 31

Discuss the applications of confidence interval estimation
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 mean volume. The historical standard deviation is 5 milliliters. In filling 250-milliliter bottles, a sample of 20 found a meanvolume of 242 milliliters. $$\begin{array} { | l | l | } \hline \text { Velvetta Inc. Shamp o0 } & \\\text { Production } & \\\hline \text { Alpha Vahe } & 0.05 \\\hline \text { Standard Deviation } & 5 \\\hline \text { Sample Size } & 20 \\\hline \text { Sample Mean } & 242 \\\hline\end{array}$$

-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 32

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 33

In the equation for calculating a confidence interval for a proportion, $p \pm z _ { a / 2 } \sqrt { \frac { p ( 1 - p ) } { n } }$ what does $\sqrt { \frac { p ( 1 - p ) } { n } }$ 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 34

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 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

Discuss the applications of confidence interval estimation
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 mean volume. The historical standard deviation is 5 milliliters. In filling 250-milliliter bottles, a sample of 20 found a meanvolume of 242 milliliters. $$\begin{array} { | l | l | } \hline \text { Velvetta Inc. Shamp o0 } & \\\text { Production } & \\\hline \text { Alpha Vahe } & 0.05 \\\hline \text { Standard Deviation } & 5 \\\hline \text { Sample Size } & 20 \\\hline \text { Sample Mean } & 242 \\\hline\end{array}$$

-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 37

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 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 38

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 39

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 40

Convenience sampling is an example of a probabilistic sampling method.

Question 41

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

Question 42

Explain selecting a sample using the continuous process sampling methods.

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

What is a confidence interval in sampling?

Question 49

Compare between a prediction interval and a confidence interval.

Question 50

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

Question 51

Estimators are the measures used to estimate population parameters.

Question 52

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

Question 53

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