Question 1

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

Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size becomes larger. Therefore, for large sample sizes (usually considered to be greater than or equal to 30), the sampling distribution of the sample mean will be approximately normal regardless of the shape of the population distribution.

Question 2

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

Accepted Answer

The spread of the sampling distribution is smaller than the spread of the corresponding population distribution because the standard error of the mean decreases as sample size increases, therefore reducing the variability of the sampling distribution.

Question 3

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue.The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What is the probability that at least 30 accounts will be classified as delinquent?

Accepted Answer

The answer of The internal auditing staff of a local...

Question 4

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at least 3.16 inches?

Accepted Answer

Since we are working with a sample size of 3, we can use the t-distribution to calculate the probability. First, we need to calculate the standard error:

SE = sqrt(0.03/3) = 0.0975

Next, we need to calculate the t-value associated with a mean of 3.16 inches:

t = (3.16 - 3) / 0.0975*sqrt(3) = 2.69

Using a t-table with 2 degrees of freedom (n-1), we find that the probability of t being greater than 2.69 is approximately 0.0548 or 5.48%. Therefore, the answer is B.

Question 5

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

Accepted Answer

As per the Central Limit Theorem, as the sample size (n) increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the population distribution, given a sufficiently large sample size.

Question 6

According to a hospital administrator,historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted. Sixty-four (64)patients indicated that they were dissatisfied with the after surgery care.What are the mean and the standard deviation of the sampling distribution of  ?

Accepted Answer

The answer of According to a hospital administrator,historical records over...

Question 7

If a sample size is at least _____,then for any sampled population,we can conclude that the sample means are approximately normal.

Accepted Answer

According to the central limit theorem, if the sample size is at least 30, then the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution. Therefore, choice C) 30 is the best choice.

Question 8

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at most 3.1 inches?

Accepted Answer

The sampling distribution of the mean has a mean of 3 inches and a standard deviation of sqrt(0.03/3). Using the Z-score formula, the Z-score for 3.1 inches is (3.1-3)/(sqrt(0.03/3)) = 1. The probability of a Z-score less than or equal to 1 is approximately 0.8413 or 84.13%.

Question 9

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue.The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What are the mean and the standard deviation of the sampling distribution of  ?

Accepted Answer

The answer of The internal auditing staff of a local...

Question 10

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue.The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What is the probability that no more than 40 accounts will be classified as delinquent?

Accepted Answer

The probability can be calculated using the normal approximation to the binomial distribution. With a sample size of 250 and a historical delinquency rate of 13%, the expected number of delinquent accounts is 32.5. The standard deviation is approximately 5.34. Using the normal distribution, the probability of having 40 or fewer delinquent accounts is approximately 92.07%.

Question 11

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 _______________.

Accepted Answer

The Central Limit Theorem states that when the sample size is large enough (typically n ≥ 30), the sampling distribution of the mean of a random sample from any population will be approximately normal, regardless of the shape of the population distribution. This theorem is used to approximate probabilities for sample means and proportions using the normal distribution. Therefore, the correct answer is D.

Question 12

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

Accepted Answer

The Central Limit Theorem states that if the sample size is sufficiently large, then the sample means are approximately normally distributed regardless of the underlying population distribution.

Question 13

According to a hospital administrator,historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted. What is the probability that at least 70 patients will not be satisfied with the after-surgery care?

Accepted Answer

The probability that at least 70 out of 400 patients are dissatisfied can be calculated using the binomial distribution with n=400 and p=0.2. The probability of 70 or more dissatisfied patients is approximately 89.44%.

Question 14

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

Accepted Answer

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

Question 15

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

The answer of In a manufacturing process a machine produces...

Question 16

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

Accepted Answer

According to the central limit theorem, when the sample size is sufficiently large, the sampling distribution of the sample proportion is approximately normal with a mean equal to the true population proportion p. Therefore, the mean of the sampling distribution of the sample proportion is equal to p * n.

Question 17

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

Accepted Answer

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

Question 18

According to a hospital administrator,historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted. What is the probability that less than 64 patients will not be satisfied with the after-surgery care?

Accepted Answer

The probability of a patient being dissatisfied with after-surgery care is 0.20. We are asked to find the probability that less than 64 patients will not be satisfied with the after-surgery care, which is the same as finding the probability that 64 or more patients will be satisfied.
The sample size n = 400 and the probability of dissatisfaction p = 0.20.
We can use the normal approximation to the binomial distribution, with mean np = 80 and standard deviation sqrt(np(1-p)) = 7.97.
To find the probability that 64 or more patients will be satisfied, we can calculate the z-score:
z = (x - np) / sqrt(np(1-p))
where x = 336 (number of satisfied patients in the sample).
z = (336 - 80) / 7.97 = 50.68
Using the normal distribution table, the probability of getting a z-score of 50.68 or higher is very small, approximately 0.0228.
Therefore, the probability that less than 64 patients will not be satisfied with the after-surgery care is 0.0228 or 2.28%. So, the correct answer is B.

Question 19

If the sampled population is finite and at least _____ times larger than the sample size,the standard deviation of  decreases as the sample size increases.

Accepted Answer

As the sampled population is finite, increasing the sample size also increases the proportion of the population being sampled, resulting in a decreased standard deviation. The finite population correction factor should be applied when the sampled population is less than 20 times the sample size. Therefore, if the population is at least 20 times larger than the sample size, the standard deviation will decrease as the sample size increases. Among the given options, only choice B meets this criterion.

Question 20

If we wish to estimate a population parameter by using a sample statistic,we are using _____.

Accepted Answer

Point estimation involves using a sample statistic to estimate a population parameter, which is what the question is asking for. Cluster sampling involves dividing a population into smaller groups, while random sampling involves selecting individuals from a population at random. Response bias refers to the tendency of individuals to answer questions in a way that they think will please the questioner, rather than answering truthfully.

Quiz 7: Sampling and Sampling Distributions

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

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

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at least 3.16 inches?

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

If a sample size is at least _____,then for any sampled population,we can conclude that the sample means are approximately normal.

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at most 3.1 inches?

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 _______________.

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

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

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the standard deviation of the sampling distribution of the sample mean?

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

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

If the sampled population is finite and at least _____ times larger than the sample size,the standard deviation of decreases as the sample size increases.

If we wish to estimate a population parameter by using a sample statistic,we are using _____.

Quiz 7: Sampling and Sampling Distributions

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

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

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at least 3.16 inches?

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

If a sample size is at least _____,then for any sampled population,we can conclude that the sample means are approximately normal.

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the probability the mean length of the bolt is at most 3.1 inches?

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 _______________.

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

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

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process: What is the standard deviation of the sampling distribution of the sample mean?

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

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

If the sampled population is finite and at least _____ times larger than the sample size,the standard deviation of decreases as the sample size increases.

If we wish to estimate a population parameter by using a sample statistic,we are using _____.

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