Question 1

The following data was collected from a simple random sample of a population. $$\begin{array} { l l l l l } 
13 & 15 & 14 & 16 & 12
\end{array}$$ The point estimate of the population standard deviation is

Accepted Answer

The point estimate of the population standard deviation is calculated using the sample standard deviation formula. The sample standard deviation for the data set {13, 15, 14, 16, 12} is approximately 1.581.

Question 2

Four hundred people were asked whether gun laws should be more stringent.Three hundred said "yes," and 100 said "no".The point estimate of the proportion in the population who will respond "no" is

Accepted Answer

The point estimate of the proportion in the population who will respond "no" is the proportion of the sample who responded "no". In this case, that would be 100/400 = 0.25 or 25%. Therefore, the correct choice is B) 0.25.

Question 3

Doubling the size of the sample will

Accepted Answer

According to the formula for calculating the standard error of the mean, the standard error is inversely proportional to the square root of the sample size. Doubling the sample size will increase the square root of the sample size by approximately 1.41 (sqrt(2)), resulting in a reduction of the standard error to approximately 70% of its current value.

Question 4

Four hundred people were asked whether gun laws should be more stringent.Three hundred said "yes," and 100 said "no".The point estimate of the proportion in the population who will respond "yes" is

Accepted Answer

The point estimate of the proportion in the population who will respond "yes" is equal to the proportion of the sample who responded "yes." In this case, 300 out of 400 respondents said "yes," so the proportion is 300/400 = 0.75. Therefore, the correct choice is C, which is the decimal equivalent of the proportion.

Question 5

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever

Accepted Answer

The sampling distribution of the sample proportion can be approximated by a normal distribution when both np and n(1-p) are greater than or equal to 5, ensuring that there are enough successes and failures in the sample.

Question 6

The following information was collected from a simple random sample of a population. 16
19
18
17
20
18
The point estimate of the mean of the population is

Accepted Answer

The point estimate of the population mean is the sample mean, which is calculated by adding up all the values in the sample and dividing by the sample size. In this case, the sample mean is (16+19+18+17+20+18)/6 = 18. Therefore, the best choice is A, which corresponds to the point estimate of 18.0.

Question 7

The number of different simple random samples of size 5 that can be selected from a population of size 8 is

Accepted Answer

The number of different simple random samples of size 5 is given by the combination formula: 
$${8 \choose 5} = \frac{8!}{5!(8-5)!} = 56$$
Therefore, the correct answer is option D.

Question 8

How many different samples of size 3 can be taken from a finite population of size 10?

Accepted Answer

The answer of How many different samples of size 3...

Question 9

The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the

Accepted Answer

The statement is based on the central limit theorem, which states that with a large enough sample size, the sampling distribution of sample means will approach a normal distribution regardless of the distribution of the population.

Question 10

The following data was collected from a simple random sample of a population. $$\begin{array} { l l l l l } 
13 & 15 & 14 & 16 & 12
\end{array}$$ If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

Accepted Answer

The number of different random samples of size 6 that can be drawn from a population of 10 elements is calculated using the combination formula $\binom{n}{r} = \frac{n!}{r!(n-r)!}$, where $n$ is the total number of elements in the population and $r$ is the sample size. Here, $\binom{10}{6} = \frac{10!}{6!4!} = 210$.

Question 11

A random sample of 121 bottles of cologne showed an average content of 4 ounces.It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.The point estimate of the mean content of the bottles is

Accepted Answer

The point estimate of the mean content of the bottles is the sample mean, which is given as 4 ounces in the question.

Question 12

As the sample size increases, the variability among the sample means

Accepted Answer

As the sample size increases, the standard error of the mean decreases, which means that the variability among the sample means also decreases. This is because larger sample sizes provide more precise estimates of the population mean, thus reducing the chance of sampling error.

Question 13

Cluster sampling is

Accepted Answer

Cluster sampling is a probability sampling method where the population is divided into clusters or groups, and a random sample of these clusters is selected. Then, all individuals in the selected clusters are included in the sample. This method is commonly used when it is impractical or too expensive to sample individuals directly, and it allows for greater efficiency in data collection.

Question 14

The following information was collected from a simple random sample of a population. $$\begin{array} { l l l l l l } 
16 & 19 & 18 & 17 & 20 & 18
\end{array}$$ The point estimate of the population standard deviation is

Accepted Answer

The point estimate of the population standard deviation is calculated using the sample standard deviation formula. The sample standard deviation for the given data is approximately 1.414.

Question 15

The following data was collected from a simple random sample of a population. $$\begin{array} { l l l l l } 
13 & 15 & 14 & 16 & 12
\end{array}$$ The point estimate of the population mean

Accepted Answer

The point estimate of the population mean is the sample mean, which is calculated as the sum of the sample values divided by the number of values: (13+15+14+16+12)/5 = 14.

Question 16

The following data was collected from a simple random sample of a population. $$\begin{array} { l l l l l } 
13 & 15 & 14 & 16 & 12
\end{array}$$ The mean of the population

Accepted Answer

The mean of the sample is 14, but the mean of the population could be any value since the sample is only a subset of the population.

Question 17

A random sample of 121 bottles of cologne showed an average content of 4 ounces.It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.The standard error of the mean equals

Accepted Answer

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size: 0.22 / √121 = 0.0200.

Question 18

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.Which of the following best describes the form of the sampling distribution of the sample mean for this situation?

Accepted Answer

The answer of Random samples of size 17 are taken...

Question 19

The sampling distribution of the sample means

Accepted Answer

The sampling distribution of the sample means shows all possible values of the sample mean for all possible samples of a certain size taken from a population. It is a probability distribution used to make inferences about the population mean, but it is not itself an estimator or estimator of the population mean.

Question 20

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.The mean and the standard deviation of the sampling distribution of the sample means are

Accepted Answer

The mean of the sampling distribution of sample means is equal to the population mean: 36. The standard deviation of the sampling distribution of sample means can be calculated using the formula: standard deviation = population standard deviation/square root of sample size. In this case, the standard deviation would be 8/square root of 17, which is approximately 1.86, so the answer is C.

Quiz 7: Sampling and Sampling Distributions

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ The point estimate of the population standard deviation is

Four hundred people were asked whether gun laws should be more stringent.Three hundred said "yes," and 100 said "no".The point estimate of the proportion in the population who will respond "no" is

Doubling the size of the sample will

Four hundred people were asked whether gun laws should be more stringent.Three hundred said "yes," and 100 said "no".The point estimate of the proportion in the population who will respond "yes" is

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the mean of the population is

The number of different simple random samples of size 5 that can be selected from a population of size 8 is

How many different samples of size 3 can be taken from a finite population of size 10?

The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

A random sample of 121 bottles of cologne showed an average content of 4 ounces.It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.The point estimate of the mean content of the bottles is

As the sample size increases, the variability among the sample means

Cluster sampling is

The following information was collected from a simple random sample of a population. $\begin{array} { l l l l l l } 16 & 19 & 18 & 17 & 20 & 18\end{array}$ The point estimate of the population standard deviation is

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ The point estimate of the population mean

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ The mean of the population

A random sample of 121 bottles of cologne showed an average content of 4 ounces.It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.The standard error of the mean equals

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.Which of the following best describes the form of the sampling distribution of the sample mean for this situation?

The sampling distribution of the sample means

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.The mean and the standard deviation of the sampling distribution of the sample means are

Quiz 7: Sampling and Sampling Distributions

The following data was collected from a simple random sample of a population. 1315141612\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}13​15​14​16​12​ The point estimate of the population standard deviation is

Four hundred people were asked whether gun laws should be more stringent.Three hundred said "yes," and 100 said "no".The point estimate of the proportion in the population who will respond "no" is

Doubling the size of the sample will

Four hundred people were asked whether gun laws should be more stringent.Three hundred said "yes," and 100 said "no".The point estimate of the proportion in the population who will respond "yes" is

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the mean of the population is

The number of different simple random samples of size 5 that can be selected from a population of size 8 is

How many different samples of size 3 can be taken from a finite population of size 10?

The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the

The following data was collected from a simple random sample of a population. 1315141612\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}13​15​14​16​12​ If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

A random sample of 121 bottles of cologne showed an average content of 4 ounces.It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.The point estimate of the mean content of the bottles is

As the sample size increases, the variability among the sample means

Cluster sampling is

The following information was collected from a simple random sample of a population. 161918172018\begin{array} { l l l l l l } 16 & 19 & 18 & 17 & 20 & 18\end{array}16​19​18​17​20​18​ The point estimate of the population standard deviation is

The following data was collected from a simple random sample of a population. 1315141612\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}13​15​14​16​12​ The point estimate of the population mean

The following data was collected from a simple random sample of a population. 1315141612\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}13​15​14​16​12​ The mean of the population

A random sample of 121 bottles of cologne showed an average content of 4 ounces.It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.The standard error of the mean equals

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.Which of the following best describes the form of the sampling distribution of the sample mean for this situation?

The sampling distribution of the sample means

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8.The mean and the standard deviation of the sampling distribution of the sample means are

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ The point estimate of the population standard deviation is

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

The following information was collected from a simple random sample of a population. $\begin{array} { l l l l l l } 16 & 19 & 18 & 17 & 20 & 18\end{array}$ The point estimate of the population standard deviation is

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ The point estimate of the population mean

The following data was collected from a simple random sample of a population. $\begin{array} { l l l l l } 13 & 15 & 14 & 16 & 12\end{array}$ The mean of the population