Business Statistics - Chapter 7: Sampling and Sampling Distributions Quiz

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 mean from that sample will be larger than 82 is _____. a) .0228 b) .4772 c) .5228 d) .9772

a) .0228

The expected value of x̄ equals the mean of the population from which the sample is drawn _____. a) for any sample size b) only if the sample size is 100 or greater c) only if the sample size is 50 or greater d) only if the sample size is 30 or greater

a) for any sample size

The probability distribution of all possible values of the sample proportion p̄ is the _____. a) sampling distribution of p̄ b) same as p̄, since it considers all possible values of the sample proportion c) sampling distribution of x̄ d) probability density function of p̄

a) sampling distribution of p̄

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is _____. a) systematic sampling b) convenience sampling c) stratified random sampling d) cluster sampling

a) systematic sampling

The basis for using a normal probability distribution to approximate the sampling distribution of x̄ and p̄ is _____. a) the central limit theorem b) Bayes' theorem c) the empirical rule d) Chebyshev's theorem

a) the central limit theorem

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is .3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is _____. a) .3000 b) .0200 c) .0004 d) .2100

b) .0200

A population of size 1,000 has a proportion of .5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are _____. a) 500 and .047 b) .5 and .047 c) 500 and .050 d) .5 and .050

b) .5 and .047

Random samples of size 36 are taken from a process (an infinite population) whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample mean are _____. a) 36 and 15 b) 20 and 2.5 c) 20 and 15 d) 20 and 0.4117

b) 20 and 2.5

Whenever the population has a normal probability distribution, the sampling distribution of x̄ is a normal probability distribution for _____. a) only samples of size 30 or greater b) any sample size c) only large sample sizes d) only small sample sizes

b) any sample size

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) decreases

The value of the ___________ is used to estimate the value of the population parameter. a) population statistic b) sample statistic c) sample parameter d) population estimate

b) sample statistic

Stratified random sampling is a method of selecting a sample in which _____. a) the sample is first divided into groups, and then random samples are taken from each group b) the population is first divided into groups, and then random samples are drawn from each group c) various strata are selected from the sample d) None of these answers are correct.

b) the population is first divided into groups, and then random samples are drawn from each group

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means _____. a) The correction factor is not necessary if the population has a normal distribution. 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) whenever the population is infinite

b) whenever the sample size is more than 5% of the population size

The sample statistic s is the point estimator of _____. a) x̄ b) σ c) μ d) p̄

b) σ

A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals .85. The probability that the sample proportion will be between .9115 and .946 is _____. a) .8633 b) .6900 c) .0819 d) .0345

c) .0819

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

c) 15

Excel's RAND function _____. a) selects a simple random sample b) determines sample size c) generates random numbers d) randomizes a population

c) generates random numbers

A sample statistic, such as x̄, that estimates the value of the corresponding population parameter is known as a _____. a) population parameter b) parameter c) point estimator d) parameter and a population parameter

c) point estimator

The standard deviation of all possible x̄ values is called the _____. a) mean deviation b) standard error of proportion c) standard error of the mean d) central variation

c) standard error of the mean

The sample mean is the point estimator of _____. a) p̄ b) x̄ c) μ d) σ

c) μ

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 normality theorem d) central limit theorem

d) central limit theorem

Convenience sampling is an example of _____. a) probabilistic sampling b) stratified sampling c) cluster sampling d) nonprobability sampling technique

d) nonprobability sampling technique

As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever _____. a) n(1 − p) ≥ 5 b) n ≥ 30 c) np ≥ 5 d) np ≥ 5 and n(1 − p) ≥ 5

d) np ≥ 5 and n(1 − p) ≥ 5

The probability distribution of all possible values of the sample mean is called the ____. a) central probability distribution b) standard error c) random variation d) sampling distribution of the sample mean

d) sampling distribution of the sample mean

The standard deviation of x̄ is referred to as the _____. a) standard x b) sample standard mean c) sample mean deviation d) standard error of the mean

d) standard error of the mean