BUS 281: Chapter 7 - Sampling and Sampling Distributions

A population has a mean of 50 and a standard deviation of 10. A random sample of 256 is selected. The standard error of x̄ is equal to ________. a) 0.625 b) 10 c) 50 d) 144

a) 0.625

A population has a mean of 100 and a standard deviation of 10. A random sample of 25 is selected. The expected value of x̄ is equal to ___________. a) 25 b) 100 c) 10 d) 2

b) 100

A sporting goods manufacturer wants to ensure that the balls it produces have a diameter of 30 inches. The standard deviation is 0.5 inches. The manufacturer samples 25 balls every 5 hours and calculates the mean diameter. The lower control limit is ________ inches. a) 29.5 b) 20.0 c) 29.7 d) 30.0

c) 29.7

In general, the control limits of a control chart are set at ____ standard deviations from the centerline. a) 1 b) 4 c) 2 d) 3

d) 3

As a general guideline, the normal distribution approximation can be used to describe the sampling distribution of the sample mean when ______________. a) n≥100 b) np≥5 and n(1-p)≥5 c) n≥5/p d) n≥30

d) n≥30

In general, the two approaches that are used for statistical quality control are __________________. -acceptance sampling and the detection approach -correlated sampling and assignable variation -chance variation and assignable variation -the regression approach and chance variation

-acceptance sampling and the detection approach

True or false: A production process is in control if the sample means on a control chart start below the centerline, trend upward, and do not cross the upper control limit.

-False

The theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large is known as the _____________. -Chebyshev's theorem -empirical rule -central limit theorem -n ≥ 30 theorem

-central limit theorem

A sporting goods manufacturer wants to ensure that the balls it produces have a diameter of 30 inches. The standard deviation is 0.5 inches. The manufacturer samples 25 balls every 5 hours and calculates the mean diameter. The upper control limit is ________ inches. a) 30.3 b) 30.5 c) 40.0 d) 30.0

a) 30.3

A population has a mean of 100 and a standard deviation of 12. A random sample of 36 is selected. The standard error of x̄ is equal to _____________. a) 10 b) 2 c) 4 d) 12

b) 2

The general rule for using the finite correction factor is that the sample constitutes at least ________ of the population. a) 10% b) 5% c) 25% d) 50%

b) 5%

Random samples of size 100 are taken from a population whose population proportion is 0.40. The expected value of the sample proportion is _________. a) 40 b) 0.04 c) 0.004 d) 0.40

d) 0.40

True or false: If we had access to data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.

-True

The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is BEST referred to as ______________. -correlated statistics -descriptive statistics -inferential statistics -hypothetical statistics

-inferential statistics

In _______________, the population is divided up into strata and then randomly selected observations are taken proportionately from each stratum. -cluster sampling -simple random sampling -stratified random sampling

-stratified random sampling

If we were to sample repeatedly from a given population, the average value of the sample means will equal ________________. -the population mean -the sample mean -the population mean divided by the square root on n -the sample mean minus the population mean, divided by the standard error of the mean

-the population mean

Which of these is a characteristic of a "bad" sample? -The sample is not representative of the population we are trying to describe -The statistic computed from the sample has no selection bias -The sample is typical of information in the population in a systematic way -The statistic computed from sample has no nonresponse bias

-The sample is not representative of the population we are trying to describe

True or false: Chance variation is not usually under the control of an individual worker or machine.

-True

Bias can occur in sampling. Bias refers to _______________. -the tendency of a sample statistics to systematically over- or under-estimate a population parameter -the use of cluster sampling instead of stratified random sampling -the creation of strata which are proportional to the stratum's size -the division of the population into overlapping groups.

-the tendency of a sample statistics to systematically over- or under-estimate a population parameter

Selection bias occurs when ______ -the population has been divided into strata -cluster sampling is used instead of stratified random sampling -cluster sampling is used instead of stratified random sampling -there is a systematic exclusion of certain groups from consideration for the sample -those responding to a survey or poll differ systematically from the non-respondents

-there is a systematic exclusion of certain groups from consideration for the sample

A control chart is a plot of calculated statistics of a production process over _______.

-time

If the population from which the sample is drawn is normally distributed, then the sampling distribution of the sample mean is ____________. -unknown -never normally distributed -always normally distributed -only sometimes normally distributed

-always normally distributed

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes ________. -larger -more spread out than a normal distribution -smaller -closer to a normal distribution

-closer to a normal distribution

The value of the finite population correction factor is always _________. -equal to zero -greater than one -less than one -less than zero

-less than one

As the sample size increases, the shape of the sampling distribution of p becomes ___________. -more normal -more skewed -less normal -less symmetric

-more normal

A population has a mean of 50 and a standard deviation of 10. A random sample of 144 is selected. The expected value of x̄ is equal to _______. a) 144 b) 50 c) 10 d) 0.625

b) 50

When a firm applies statistical techniques to develop and maintain its ability to produce high-quality goods and services, it is implementing statistical __________. -quality control -correction factors -standard errors -cluster sampling

-quality control

A population consists of all items of interest in a statistical problem, whereas a ___________ is a subset of the population. -census -probability -sample -parameter

-sample

The probability distribution of the sample mean is commonly referred to as the ___________. -sampling distribution of of p -sampling distribution of of σ -sampling distribution of of μ -sampling distribution of of x̄

-sampling distribution of of x̄

Assignable variation is caused by __________________. -randomly occurring events in the production process -specific events that can usually be identified and eliminated -events that are not preventable

-specific events that can usually be identified and eliminated

We use a calculated sample ________ to make inferences about an unknown population ________. -statistic, parameter -statistic, statistic -parameter, parameter -parameter, statistic

-statistic, parameter

Stratified sampling is preferred to cluster sampling when the objective is ________. -to increase precision -to access every possible individual in the population -to reduce costs

-to increase precision