Question 1

For large samples,the sampling distribution of  is approximately normal with a mean of _____.
A) μ
B) μ/√n
C)
D) z

Accepted Answer

The answer of For large samples,the sampling distribution of ...

Question 2

Whenever the population has a normal distribution,the sampling distribution of is a normal or near normal distribution
A) for only large sample sizes.
B) for only small sample sizes.
C) for any sample size.
D) for only samples of size 30 or more.

Accepted Answer

The central limit theorem states that regardless of the population distribution, as the sample size increases, the sampling distribution of the mean approaches a normal distribution. Therefore, the sampling distribution of means is a normal or near-normal distribution for any sample size as long as the population distribution is normal.

Question 3

The population of all sample proportions has a normal distribution if the sample size (n)is sufficiently large.The rule of thumb for ensuring that n is sufficiently large is
A) np ≥ 5.
B) n(1 − p)≥ 5.
C) np ≤ 5.
D) n(1 − p)≤ 5 and np ≤ 5.
E) np ≥ 5 and n(1 − p)≥ 5.

Accepted Answer

The rule of thumb for ensuring that the sample size (n) is sufficiently large for a normal distribution of sample proportions is when both np ≥ 5 and n(1-p) ≥ 5. This ensures that the expected number of successes (np) and failures (n(1-p)) are both large enough to approximate a normal distribution. Therefore, option E is the best choice as it includes both np and n(1-p) being greater than or equal to 5.

Question 4

Consider a sampling distribution formed based on n = 3.The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements σ.
A) always
B) sometimes
C) never

Accepted Answer

According to the Central Limit Theorem, as the sample size increases, the standard deviation of the sampling distribution of the sample means decreases. Therefore, as n = 3 is a small sample size, the standard deviation of the population of all sample means will always be less than the standard deviation of the population of individual measurements σ.

Question 5

The sample standard deviation s is an unbiased estimator of the population standard deviation σ.

Accepted Answer

There is no way to calculate an unbiased estimate of σ.

Question 6

The sampling distribution of the sample mean is a normal distribution for ________ sample sizes,regardless of the shape of the corresponding population distribution.
A) random
B) large
C) larger than 50
D) small

Accepted Answer

The Central Limit Theorem states that for large sample sizes (generally considered to be 30 or greater), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

Question 7

____________ says that if the sample size is sufficiently large,then the sample means are approximately normally distributed.
A) Cluster sampling
B) Sampling error
C) Sampling distribution of the mean
D) The Central Limit Theorem

Accepted Answer

The Central Limit Theorem states that if the sample size is sufficiently large, the sampling distribution of the mean will be approximately normally distributed, regardless of the shape of the population distribution.

Question 8

The spread of the sampling distribution of is ____________ the spread of the corresponding population distribution sampling distribution.
A) larger than
B) smaller than
C) the same as
D) exactly ½

Accepted Answer

The spread of the sampling distribution is smaller than the spread of the corresponding population distribution because the Central Limit Theorem states that as sample size increases, the sampling distribution becomes more and more normally distributed with a smaller spread.

Question 9

If the sample size n is infinitely large,then s² is an unbiased estimator of σ².

Accepted Answer

When the sample size is infinitely large (often denoted as n → ∞), the sample standard deviation (denoted as S) converges in probability to the population standard deviation (denoted as σ). In this case, the estimator s², which is based on the sample standard deviation, also converges in probability to σ. Therefore, it is an unbiased estimator of σ.

Question 10

According to the Central Limit Theorem,if a sample size is at least _____,then for most sampled populations,we can conclude that the sample means are approximately normal.
A) 25
B) 20
C) 30
D) 50

Accepted Answer

30 is the cut off for the Central Limit Theorem.

Question 11

The Central Limit Theorem states that as the sample size increases,the distribution of the sample ____________ approaches the normal distribution.
A) medians
B) means
C) standard deviations
D) variances

Accepted Answer

The Central Limit Theorem states that as the sample size increases, the distribution of the sample means approaches the normal distribution.

Question 12

The notation for the standard deviation of the sampling distribution of the sample mean is __________.
A)
B) σx
C)
D) μ

Accepted Answer

The answer of The notation for the standard deviation of...

Question 13

There is no easy way to calculate an unbiased point estimate of σ.

Accepted Answer

This statement is true. This is because σ is a population parameter and to estimate it, one needs to have information about the entire population. However, in most cases, only a sample of the population data is available. Therefore, any estimate of σ based on the sample will be biased, meaning that it will tend to overestimate or underestimate the true value of σ. Various methods, such as the use of correction factors, can be used to account for this bias, but there is no reliable or easy way to calculate an unbiased point estimate of σ from a sample.

Question 14

As the sample size ______________,the variation of the sampling distribution of ___________.
A) decreases,decreases
B) increases,remains the same
C) decreases,remains the same
D) increases,decreases
E) None of the other choices is correct.

Accepted Answer

As the sample size increases, the variation (standard deviation) of the sampling distribution of the sample mean decreases, according to the Central Limit Theorem.

Question 15

If the sampled population is finite and at least _____ times larger than the sample size,we treat the population as infinite.
A) 5
B) 20
C) 30
D) 10

Accepted Answer

According to statistical theory, if the sampled population is finite, we treat the population as infinite if it is at least 20 times larger than the sample size. Therefore, option B is the best choice as it satisfies this requirement.

Question 16

If a population distribution is known to be normal,then it follows that
A) the sample mean must equal the population mean.
B) the sample mean must equal the population mean for large samples.
C) the sample standard deviation must equal the population standard deviation.
D) the sample mean must equal the population mean,the sample mean must equal the population mean for large samples,and the sample standard deviation must equal the population standard deviation.
E) None of the other choices is correct.

Accepted Answer

The answer of If a population distribution is known to...

Question 17

The quantity √[(N − n)(N − 1)] is called the finite population multiplier.

Accepted Answer

This is true, the quantity √[(N − n)(N − 1)] is indeed called the finite population multiplier.

Question 18

If the sampled population has a mean of 48 and standard deviation of 16,then the mean and the standard deviation for the sampling distribution of for n = 16 are
A) 4 and 1.
B) 12 and 4.
C) 48 and 4.
D) 48 and 1.
E) 48 and 16.

Accepted Answer

The mean of the sampling distribution will be the same as the population mean, which is 48. The standard deviation of the sampling distribution can be calculated by dividing the population standard deviation by the square root of the sample size, which is 16^(1/2) = 4. Therefore, the answer is choice C, with a mean of 48 and standard deviation of 4.

Question 19

For nonnormal populations,as the sample size (n)___________________,the distribution of sample means approaches a(n)________________ distribution.
A) decreases,uniform
B) increases,normal
C) decreases,normal
D) increases,uniform
E) increases,exponential

Accepted Answer

As the sample size increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the population distribution.

Question 20

The mean of the sampling distribution of the sample proportion is equal to _____ when the sample size is sufficiently large.
A) μ
B) p
C) p × n
D) (1 − p)

Accepted Answer

The sample proportion will approximate the population proportion.

Quiz 7: Sampling and Sampling Distributions

For large samples,the sampling distribution of is approximately normal with a mean of _____.

Whenever the population has a normal distribution,the sampling distribution of is a normal or near normal distribution

The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large.The rule of thumb for ensuring that n is sufficiently large is

Consider a sampling distribution formed based on n = 3.The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements σ.

The sample standard deviation s is an unbiased estimator of the population standard deviation σ.

The sampling distribution of the sample mean is a normal distribution for ________ sample sizes,regardless of the shape of the corresponding population distribution.

____________ says that if the sample size is sufficiently large,then the sample means are approximately normally distributed.

The spread of the sampling distribution of is ____________ the spread of the corresponding population distribution sampling distribution.

If the sample size n is infinitely large,then s² is an unbiased estimator of σ².

According to the Central Limit Theorem,if a sample size is at least _____,then for most sampled populations,we can conclude that the sample means are approximately normal.

The Central Limit Theorem states that as the sample size increases,the distribution of the sample ____________ approaches the normal distribution.

The notation for the standard deviation of the sampling distribution of the sample mean is __________.

There is no easy way to calculate an unbiased point estimate of σ.

As the sample size ____,the variation of the sampling distribution of _.

If the sampled population is finite and at least _____ times larger than the sample size,we treat the population as infinite.

If a population distribution is known to be normal,then it follows that

The quantity √[(N − n)(N − 1)] is called the finite population multiplier.

If the sampled population has a mean of 48 and standard deviation of 16,then the mean and the standard deviation for the sampling distribution of for n = 16 are

For nonnormal populations,as the sample size (n) ___,the distribution of sample means approaches a(n) distribution.

The mean of the sampling distribution of the sample proportion is equal to _____ when the sample size is sufficiently large.

Quiz 7: Sampling and Sampling Distributions

For large samples,the sampling distribution of is approximately normal with a mean of _____.

Whenever the population has a normal distribution,the sampling distribution of is a normal or near normal distribution

The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large.The rule of thumb for ensuring that n is sufficiently large is

Consider a sampling distribution formed based on n = 3.The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements σ.

The sample standard deviation s is an unbiased estimator of the population standard deviation σ.

The sampling distribution of the sample mean is a normal distribution for ________ sample sizes,regardless of the shape of the corresponding population distribution.

____________ says that if the sample size is sufficiently large,then the sample means are approximately normally distributed.

The spread of the sampling distribution of is ____________ the spread of the corresponding population distribution sampling distribution.

If the sample size n is infinitely large,then s2 is an unbiased estimator of σ2.

According to the Central Limit Theorem,if a sample size is at least _____,then for most sampled populations,we can conclude that the sample means are approximately normal.

The Central Limit Theorem states that as the sample size increases,the distribution of the sample ____________ approaches the normal distribution.

The notation for the standard deviation of the sampling distribution of the sample mean is __________.

There is no easy way to calculate an unbiased point estimate of σ.

As the sample size ______________,the variation of the sampling distribution of ___________.

If the sampled population is finite and at least _____ times larger than the sample size,we treat the population as infinite.

If a population distribution is known to be normal,then it follows that

The quantity √[(N − n)(N − 1)] is called the finite population multiplier.

If the sampled population has a mean of 48 and standard deviation of 16,then the mean and the standard deviation for the sampling distribution of for n = 16 are

For nonnormal populations,as the sample size (n) ___________________,the distribution of sample means approaches a(n) ________________ distribution.

The mean of the sampling distribution of the sample proportion is equal to _____ when the sample size is sufficiently large.

If the sample size n is infinitely large,then s² is an unbiased estimator of σ².

As the sample size ____,the variation of the sampling distribution of _.

For nonnormal populations,as the sample size (n) ___,the distribution of sample means approaches a(n) distribution.