Question 1

As a general rule, 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 sufficient sample size for both successes and failures.

Question 2

The probability distribution of all possible values of the sample proportion  is the

Accepted Answer

The probability distribution of all possible values of the sample proportion is the sampling distribution of the proportion, which is represented by choice D. Choice A is incorrect because a probability density function is used to describe continuous random variables, but the sample proportion is a discrete random variable. Choice B is incorrect because the sampling distribution of the mean typically pertains to continuous data, whereas we are dealing with a proportion here. Choice C is incorrect because the probability distribution of the sample proportion only considers all possible values of the proportion, not all possible values of the population proportion.

Question 3

The population we want to make inferences about is the

Accepted Answer

The target population is the group of individuals or objects that we want to make inferences about based on our sample. It is the group that we are interested in studying and drawing conclusions about, rather than just the group that we happen to have data on.

Question 4

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were females. The standard error of the proportion of females is

Accepted Answer

The standard error of the proportion is calculated using the formula SE = sqrt[p(1-p)/n], where p is the sample proportion (90/150 = 0.6) and n is the sample size (150). SE = sqrt[0.6(0.4)/150] = 0.0400.

Question 5

Convenience sampling is an example of

Accepted Answer

Convenience sampling is a nonprobability sampling technique where participants are selected based on their availability and willingness to participate, rather than being chosen randomly. This type of sampling is frequently used in studies that are exploratory in nature or lack dedicated resources for conducting a larger more comprehensive study. Since participants are self-selected, it is not possible to estimate the probability of getting a representative sample of a population. Therefore, convenience sampling is a type of nonprobability sampling.

Question 6

Which of the following is an example of a nonprobability sampling technique?

Accepted Answer

Judgment sampling is a nonprobability sampling technique where the researcher selects individuals based on their judgment or expertise about the population being studied. The other options listed are all examples of probability sampling techniques.

Question 7

Random samples of size 100 are taken from a process (an infinite population) whose population proportion is 0.2. The mean and standard deviation of the distribution of sample proportions are

Accepted Answer

The mean of the distribution of sample proportions is equal to the population proportion, which is 0.2. The standard deviation is calculated using the formula sqrt(p(1-p)/n), where p is the population proportion and n is the sample size. So, sqrt(0.2*0.8/100) = 0.04.

Question 8

When the population has a normal distribution, the sampling distribution of  is normally distributed

Accepted Answer

The answer of When the population has a normal distribution,...

Question 9

Exhibit 7-1
The following data was collected from a simple random sample from a process (an infinite population). 
-Refer to Exhibit 7-1. 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 observations divided by the sample size. In this case, the sum of the sample observations is 140 and the sample size is 10, so the sample mean is 14.

Question 10

A sample of 400 observations will be taken from a process (an infinite population). The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

Accepted Answer

We can use the central limit theorem here since n = 400 > 30. The mean of the sample proportion is equal to the population proportion, which is 0.8. The standard deviation of the sample proportion is calculated as:
sqrt((0.8 * 0.2) / 400) = 0.02

To find the probability that the sample proportion will be greater than 0.83, we standardize the value as follows:
(0.83 - 0.8) / 0.02 = 1.5

Using a z-table, the probability of getting a z-score greater than 1.5 is 0.0668. Therefore, the answer is choice C.

Question 11

Cluster sampling is

Accepted Answer

Cluster sampling is a probability sampling method where the population is divided into clusters, and a random sample of clusters is selected. Then, all individuals within the selected clusters are included in the sample. Therefore, it is a probability sampling method. A is incorrect because cluster sampling is a probability sampling method. B is incorrect because convenience sampling is a nonprobability sampling method where the sample is selected based on convenience. D is incorrect because one of the alternatives is correct, and that is C.

Question 12

It is impossible to construct a frame for a

Accepted Answer

The answer of It is impossible to construct a frame...

Question 13

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of  is

Accepted Answer

The sampling distribution of 11ea86e1_d6f8_e228_a30f_f9f650fb0518_TB2162_11 is approximately normal if the sample size is large enough and if both np and n(1-p) are at least 5. Therefore, the best choice is C since it satisfies these conditions. The other choices either have stricter or weaker requirements for normality.

Question 14

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

Accepted Answer

The proportion remains 0.5. The standard deviation of the sample proportion is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p = 0.5$ and $n = 100$. This gives $\sqrt{\frac{0.5(1-0.5)}{100}} = \sqrt{\frac{0.25}{100}} = \sqrt{0.0025} = 0.05$. However, there seems to be a mistake in my calculation as the correct standard deviation should be 0.05, aligning with option D, not C. My explanation incorrectly supports C due to a miscalculation. The correct answer, based on the correct calculation, should be D, not C.

Question 15

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

Accepted Answer

The standard error of the proportion is given by the formula:

SE = sqrt(p*q/n)

where p is the population proportion (0.3), q = 1-p (0.7), and n is the sample size (525).

Plugging in the values, we get:

SE = sqrt(0.3*0.7/525) = 0.0200

Therefore, the standard deviation of the sample proportions is 0.0200, which corresponds to choice D.

Question 16

A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is

Accepted Answer

We are given that the population proportion is p = 0.85 and the sample size is n = 51. Also note that the sample proportion, say p_hat, follows a normal distribution with mean = p = 0.85 and standard deviation = sqrt[p(1-p)/n] = sqrt[(0.85)(0.15)/51] = 0.064.

To find the probability that the sample proportion is between 0.9115 and 0.946, we first standardize the values:
(z_1) = (0.9115 - 0.85)/0.064 = 0.9594
(z_2) = (0.946 - 0.85)/0.064 = 1.5000

Then we look up the area under the standard normal curve between these z-values:
P(0.9594 ≤ Z ≤ 1.5000) = 0.0819

Therefore, the probability that the sample proportion will be between 0.9115 and 0.946 is 0.0819, which corresponds to choice (B).

Question 17

A sample of 66 observations will be taken from a process (an infinite population). The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

Accepted Answer

The sample proportion follows a normal distribution with mean equal to the population proportion (0.12) and standard deviation equal to sqrt[(0.12)(0.88)/66]. Using the standard normal distribution, the probability that the sample proportion is less than 0.1768 corresponds to a z-score of approximately 1.42, which gives a cumulative probability of about 0.9222.

Question 18

Exhibit 7-1
The following data was collected from a simple random sample from a process (an infinite population). 
-Refer to Exhibit 7-1. 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, which is approximately equal to the sample standard deviation divided by the square root of the sample size. Plugging in the given values, we get:

s = 4.0 
n = 10

So the point estimate of the population standard deviation is approximately:

s/√n = 4.0/√10 ≈ 1.581

Therefore, the best choice is B.

Question 19

Which of the following sampling methods does not lead to probability samples?

Accepted Answer

Convenience sampling is a non-probability sampling method where the sample is selected based on the ease of accessibility. Probability sampling methods (such as stratified, cluster, and systematic sampling) ensure that every member of the population has an equal chance of being selected for the sample, while convenience sampling does not guarantee this.

Question 20

Stratified random sampling is a method of selecting a sample in which

Accepted Answer

In stratified random sampling, the population is divided into distinct subgroups or strata, and then random samples are drawn from each of these strata to ensure representation from all segments.

Quiz 7: Sampling and Sampling Distributions

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

The probability distribution of all possible values of the sample proportion is the

The population we want to make inferences about is the

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were females. The standard error of the proportion of females is

Convenience sampling is an example of

Which of the following is an example of a nonprobability sampling technique?

Random samples of size 100 are taken from a process (an infinite population) whose population proportion is 0.2. The mean and standard deviation of the distribution of sample proportions are

When the population has a normal distribution, the sampling distribution of is normally distributed

Exhibit 7-1 The following data was collected from a simple random sample from a process (an infinite population) . -Refer to Exhibit 7-1. The point estimate of the population mean

A sample of 400 observations will be taken from a process (an infinite population) . The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

Cluster sampling is

It is impossible to construct a frame for a

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

A sample of 51 observations will be taken from a process (an infinite population) . The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is

A sample of 66 observations will be taken from a process (an infinite population) . The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

Exhibit 7-1 The following data was collected from a simple random sample from a process (an infinite population) . -Refer to Exhibit 7-1. The point estimate of the population standard deviation is

Which of the following sampling methods does not lead to probability samples?

Stratified random sampling is a method of selecting a sample in which

Quiz 7: Sampling and Sampling Distributions

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

The probability distribution of all possible values of the sample proportion is the

The population we want to make inferences about is the

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were females. The standard error of the proportion of females is

Convenience sampling is an example of

Which of the following is an example of a nonprobability sampling technique?

Random samples of size 100 are taken from a process (an infinite population) whose population proportion is 0.2. The mean and standard deviation of the distribution of sample proportions are

When the population has a normal distribution, the sampling distribution of is normally distributed

Exhibit 7-1 The following data was collected from a simple random sample from a process (an infinite population) . -Refer to Exhibit 7-1. The point estimate of the population mean

A sample of 400 observations will be taken from a process (an infinite population) . The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

Cluster sampling is

It is impossible to construct a frame for a

A sample of 25 observations is taken from a process (an infinite population) . The sampling distribution of is

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

A sample of 51 observations will be taken from a process (an infinite population) . The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is

A sample of 66 observations will be taken from a process (an infinite population) . The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

Exhibit 7-1 The following data was collected from a simple random sample from a process (an infinite population) . -Refer to Exhibit 7-1. The point estimate of the population standard deviation is

Which of the following sampling methods does not lead to probability samples?

Stratified random sampling is a method of selecting a sample in which