Question 1

The central limit theorem states that as the sample size increases the distribution of the sample ________ approach 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 will approach the normal distribution regardless of the shape of the population distribution. The other options (medians, standard deviations, and variances) are not affected by the sample size, and thus are not part of the central limit theorem.

Question 2

A manufacturing company measures the weight of boxes before shipping them to the customers.If the box weights have a population mean and standard deviation of 90 lbs.and 24 lbs.respectively,then based on a sample size of 36 boxes,the probability that the average weight of the boxes will exceed 94 lbs.is:
A)34.13%
B)84.13%
C)15.87%
D)56.36%
E)16.87%

Accepted Answer

We can use the central limit theorem here, which states that for a sample size n>30, the sampling distribution of the sample mean will be approximately normal with a mean of the population mean and a standard deviation of the population standard deviation/sqrt(n).

So, in this case, the mean of the sampling distribution will be 90 lbs and the standard deviation will be 24/sqrt(36) = 4 lbs.

Now, we need to find the probability that the sample mean will be greater than 94 lbs:

z = (94 - 90) / 4 = 1

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score greater than 1 is 0.1587.

Therefore, the probability that the average weight of the boxes will exceed 94 lbs is 15.87%. Thus, the best choice is C.

Question 3

If we have a sample size of 100 and the estimate of the population proportion is .10,the mean of the sampling distribution of the sample proportion is:
A)0.0009
B)0.10
C)0.03
D)0.90
E)0.09

Accepted Answer

The mean of the sampling distribution of the sample proportion (p-hat) is equal to the population proportion (p), which is 0.10 in this case. Therefore, the best choice is B.

Question 4

The mean of the sampling distribution of  is always equal to the mean of the sampled population.

Accepted Answer

According to the Central Limit Theorem, if the sample size is sufficiently large, the mean of the sampling distribution will be equal to the mean of the population from which it is drawn. Therefore, the statement is true.

Question 5

_____________ is the difference between a numerical description of the population and the corresponding descriptor of the sample.
A)Sampling error
B)Non-observation error
C)Observation error
D)Non-response

Accepted Answer

Sampling error is the difference between a numerical description of the population and the corresponding descriptor of the sample. Non-observation error refers to cases where an individual or group is not included in the sample. Observation error occurs when there are errors in the measurement or recording of data. Non-response refers to cases where someone chosen for the sample does not participate or respond to the survey or study.

Question 6

A 'Yes or No' question is _____________.
A)Dichotomous
B)Multiple Choice
C)Open-ended
D)Systematic

Accepted Answer

A 'Yes or No' question is known as a dichotomous question because it offers only two response options. Multiple choice questions provide more than two options, open-ended questions have no specific response options, and systematic questions typically refer to a method or approach rather than a type of question.

Question 7

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 $\ge$ 5
B)n(1 - p)5
C)np $\le$ 5
D)n(1 - p)$\le$ .5 and np $\le$ 5
E)np .5 and n(1 - p)$\ge$ 5

Accepted Answer

The rule of thumb for the normal approximation to be valid is that both np and n(1-p) should be at least 5.

Question 8

If the sampled population has a mean 48 and standard deviation 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 of sample means (also known as the central limit theorem) is equal to the mean of the population, which is given as 48. Thus, the mean of the sampling distribution for n = 16 is also 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^.5 or approximately 4. Thus, the standard deviation of the sampling distribution for n = 16 is 4. Therefore, the best choice is option C.

Question 9

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  $\sigma$.
A)Always
B)Sometimes
C)Never

Accepted Answer

The answer of Consider a sampling distribution formed based on...

Question 10

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

Accepted Answer

When the sample size is infinitely large, the sample mean becomes an unbiased estimator of the population mean. Therefore, 11eaa0cf_06ec_387d_9cb2_fff0ab39413e_TB1737_11, which is the sample mean, will also be an unbiased estimator of 11eaa0cf_06ec_5f8e_9cb2_2792afb96f9c_TB1737_11, which is the population mean.

Question 11

A manufacturing company measures the weight of boxes before shipping them to the customers.If the box weights have a population mean and standard deviation of 90 lbs.and 24 lbs.respectively,then based on a sample size of 36 boxes,the probability that the average weight of the boxes will be less than 84 lbs.is:
A)16.87%
B)93.32%
C)43.32%
D)6.678%
E)84.13%

Accepted Answer

We can use the Central Limit Theorem since the sample size is greater than 30.

z = (x̄ - μ) / (σ /√n) where x̄ = 84, μ = 90, σ = 24, and n = 36

z = (84 - 90) / (24 / √36) = -2

Using a standard normal distribution table, we find that the probability of getting a z-score less than -2 is 0.0228 or 2.28%. Converting this to a percentage, we get 2.28 * 100% = 6.678%.

Therefore, the probability that the average weight of the boxes will be less than 84 lbs. is 6.678%. The best choice is D.

Question 12

_____________ occurs when some population elements are excluded from the process of selecting the sample.
A)Non-response
B)Error of observation
C)Undercoverage
D)Sampling error

Accepted Answer

Undercoverage occurs when certain members of the population are not represented in the sample. This can lead to biased or inaccurate results if the excluded members have different characteristics or opinions than those included in the sample. Non-response refers to individuals who refuse or are unable to participate in the sample, error of observation refers to mistakes made during data collection or recording, and sampling error refers to natural variation that occurs when taking a random sample of a population.

Question 13

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)All of the above.
E)None of the above.

Accepted Answer

A normal population distribution does not guarantee that any single sample mean or standard deviation will exactly equal the population parameters, though they may approximate them as sample size increases.

Question 14

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

Whenever the population has a normal distribution, the sampling distribution of the mean will be normal or near normal, regardless of the sample size. This is due to the central limit theorem, which states that as sample size increases, the sampling distribution of the mean becomes more normal, even for non-normal populations.

Question 15

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

Accepted Answer

The answer of The sample standard deviation s is an...

Question 16

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 above

Accepted Answer

The answer of As the sample size ______________ the variation...

Question 17

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

Accepted Answer

This statement accurately describes the process of developing the sampling distribution of the sample mean.

Question 18

A common practice in selecting a sample from a large geographic area is multi-stage cluster sampling.

Accepted Answer

Multi-stage cluster sampling involves dividing the population into clusters based on geographic location and then randomly selecting clusters to sample from. It is a common practice in selecting a sample from a large geographic area.

Question 19

If we have a sample size of 100 and the estimate of the population proportion is .10,the standard deviation of the sampling distribution of the sample proportion is:
A).0009
B).03
C)3
D)9
E).10

Accepted Answer

The formula for the standard deviation of the sampling distribution of the sample proportion is given by:
sqrt(p * (1-p) / n)
where p is the population proportion and n is the sample size.
Plugging in the values given, we get:
sqrt(0.1 * (1-0.1) / 100) = 0.03.
Therefore, the correct answer is B).03.

Question 20

A low response rate has no effect on the validity of a survey's findings.

Accepted Answer

A low response rate can lead to non-response bias, which can affect the validity of a survey's findings. Those who choose not to respond may have different opinions or characteristics than those who do respond, thus skewing the results.

Quiz 7: Sampling and Sampling Distributions

The central limit theorem states that as the sample size increases the distribution of the sample ________ approach the normal distribution.

If we have a sample size of 100 and the estimate of the population proportion is .10,the mean of the sampling distribution of the sample proportion is:

The mean of the sampling distribution of is always equal to the mean of the sampled population.

_____________ is the difference between a numerical description of the population and the corresponding descriptor of the sample.

A 'Yes or No' question is _____________.

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:

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

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

_____________ occurs when some population elements are excluded from the process of selecting the sample.

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

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

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

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

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

A common practice in selecting a sample from a large geographic area is multi-stage cluster sampling.

If we have a sample size of 100 and the estimate of the population proportion is .10,the standard deviation of the sampling distribution of the sample proportion is:

A low response rate has no effect on the validity of a survey's findings.

Quiz 7: Sampling and Sampling Distributions

The central limit theorem states that as the sample size increases the distribution of the sample ________ approach the normal distribution.

If we have a sample size of 100 and the estimate of the population proportion is .10,the mean of the sampling distribution of the sample proportion is:

The mean of the sampling distribution of is always equal to the mean of the sampled population.

_____________ is the difference between a numerical description of the population and the corresponding descriptor of the sample.

A 'Yes or No' question is _____________.

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:

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

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\sigmaσ .

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

_____________ occurs when some population elements are excluded from the process of selecting the sample.

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

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

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

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

The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.

A common practice in selecting a sample from a large geographic area is multi-stage cluster sampling.

If we have a sample size of 100 and the estimate of the population proportion is .10,the standard deviation of the sampling distribution of the sample proportion is:

A low response rate has no effect on the validity of a survey's findings.

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