Question 1

Exhibit 21-4
Simple random sampling has been used to obtain a sample of size 50 from a population of size 500. The sample proportion was 0.7.
-Refer to Exhibit 21-4. The estimate of the standard error of proportion is

Accepted Answer

The formula for estimating the standard error of proportion is:
SEp = sqrt(p(1-p)/n)
where p is the sample proportion and n is the sample size.

Plugging in the values given in the question:
SEp = sqrt(0.7(1-0.7)/50)
SEp = 0.062

Question 2

Exhibit 21-3
From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40.
-Refer to Exhibit 21-3. An approximate 95% confidence interval for the population mean is

Accepted Answer

We can use the formula for a confidence interval:
CI = sample mean ± z*(standard error)
where z is the critical value from the standard normal distribution based on the desired level of confidence (95% in this case), and the standard error is given by:
standard error = sample standard deviation / sqrt(sample size)
Plugging in the values from the question, we get:
standard error = 40 / sqrt(58) = 5.24
Using a table or calculator, we can find that the critical value z for a 95% confidence level is approximately 1.96.
Substituting into the formula for the confidence interval, we get:
CI = 400 ± 1.96*(5.24) = (389.7, 410.3)
Rounded to the nearest integer, this becomes (390, 410), which corresponds to choice D. Therefore, the best choice is D with an approximate 95% confidence interval for the population mean of 390 to 410.

Question 3

Exhibit 21-3
From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40.
-Refer to Exhibit 21-3. An estimate of the standard error of the mean is

Accepted Answer

The standard error of the mean is calculated as the sample standard deviation divided by the square root of the sample size: 40 / √58 ≈ 5.24, which rounds to 5.0.

Question 4

An unbiased estimate of the population total is given by the

Accepted Answer

The unbiased estimate of the population total is obtained by multiplying the sample mean by the size of the population. This method assumes that the sample mean is a good representation of the population mean, thus scaling it up to the population size gives an estimate of the total value in the population.

Question 5

With nonprobabilistic sampling

Accepted Answer

Nonprobabilistic sampling does not involve random selection of individuals from the population and therefore does not allow for estimation of precision or generalizability to the population.

Question 6

A version of cluster sampling in which the elements are formed into clusters on the basis of their geographic proximity is

Accepted Answer

The described method of sampling is area sampling, which involves dividing the population into geographic areas or clusters, and then selecting a sample of those areas. This method is often used when the population of interest is spread out geographically and it is not feasible or cost-effective to sample from the entire population.

Question 7

Exhibit 21-2
A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60.
-Refer to Exhibit 21-2. An approximate 95% confidence interval for the population mean is

Accepted Answer

We can use the formula for a confidence interval for the population mean as follows:

Confidence interval = sample mean ± (critical value (based on the level of confidence) × standard error of the mean)

Since the population standard deviation is unknown, we need to use the t-distribution and the degrees of freedom = n-1 = 42.

The critical value for a 95% confidence interval with 42 degrees of freedom is approximately 2.021 (found in t-table or using a calculator).

The standard error of the mean can be calculated as:

standard error of the mean = sample standard deviation / sqrt(sample size)
standard error of the mean = 60 / sqrt(43)
standard error of the mean ≈ 9.16

Therefore, the 95% confidence interval can be calculated as:

Confidence interval = 500 ± (2.021 × 9.16)
Confidence interval ≈ (482.2, 517.8)

Thus, the best choice is A) 482.2 to 517.8.

Question 8

Exhibit 21-1
A simple random sample of size 64 is taken from a population of size 800. The sample mean is determined to be 2,550 with a standard deviation of 500.
-Refer to Exhibit 21-1. The point estimate of the population total is

Accepted Answer

The answer of Exhibit 21-1
A simple random sample of size...

Question 9

Exhibit 21-3
From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40.
-Refer to Exhibit 21-3. An approximate 95% confidence interval for the population total is

Accepted Answer

The 95% confidence interval for the population total is calculated using the formula for the confidence interval of the total: Total = N * (sample mean ± margin of error), where margin of error = z * (s/√n) * √((N-n)/(N-1)). Here, N=600, n=58, sample mean=400, s=40, and z=1.96 for 95% confidence.

Question 10

Exhibit 21-2
A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60.
-Refer to Exhibit 21-2. An approximate 95% confidence interval for the population total is

Accepted Answer

To find an approximate 95% confidence interval for the population total, we need to use the formula:
Estimate ± (Critical value) × (Standard error of estimate)
where the estimate is the sample mean multiplied by the population size, the critical value is obtained from the t-distribution table with (n-1) degrees of freedom and a 95% confidence level, and the standard error of estimate is given by the formula:
Sample standard deviation / sqrt(n)
Plugging in the values, we get:
Estimate = 500 × 800 = 400,000
Standard error of estimate = 60 / sqrt(43) ≈ 9.17
Using a t-distribution table with 42 degrees of freedom (n-1), we find the critical value to be 2.021. 
Therefore, the 95% confidence interval is:
400,000 ± 2.021 × 9.17
= 400,000 ± 18,554.5
= (385,445.5, 414,554.5)
which corresponds to choice B.

Question 11

Exhibit 21-3
From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40.
-Refer to Exhibit 21-3. The population total is

Accepted Answer

To find the population total, we use the formula: Population Total = Sample Mean x Population Size. Rearranging this formula, we get: Population Size = Population Total / Sample Mean. Substituting the given values, we get: Population Size = Population Total / 400. Solving for the population size, we get: Population Size = 600. Therefore, the population total is Population Size x Sample Mean = 240,000.

Question 12

Sampling errors can

Accepted Answer

Sampling errors cannot be completely avoided because they are inherent in the process of selecting a sample from a population. Even with probabilistic sampling methods and increasing sample sizes, there is always a chance of error in estimating population parameters.

Question 13

Exhibit 21-2
A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60.
-Refer to Exhibit 21-2. The standard error of the mean is

Accepted Answer

The answer of Exhibit 21-2
A simple random sample of 43...

Question 14

Which of the following is (are) the most common type(s) of surveys?

Accepted Answer

All of these answers are correct. The most common types of surveys are mail surveys, telephone surveys, and personal interviews. Each of these methods has its own advantages and disadvantages, and the choice of which method to use will depend on the research goals and the characteristics of the target population.

Question 15

Exhibit 21-1
A simple random sample of size 64 is taken from a population of size 800. The sample mean is determined to be 2,550 with a standard deviation of 500.
-Refer to Exhibit 21-1. An estimate of the standard error of the mean (for the total) is

Accepted Answer

The answer of Exhibit 21-1
A simple random sample of size...

Question 16

Exhibit 21-2
A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60.
-Refer to Exhibit 21-2. The population total is

Accepted Answer

The formula for population total is N = n * x̄, where N is the population total, n is the sample size, and x̄ is the sample mean. Therefore, N = 43 * 500 = 21,500.

Question 17

In a sample survey, it is common practice to use a t value of (when approximating a 95% confidence interval)

Accepted Answer

A t value of 2 is commonly used when approximating a 95% confidence interval in a sample survey.

Question 18

A method of selecting a sample by randomly selecting the first element and then selecting every k^th element thereafter is

Accepted Answer

The method described is systematic sampling, where the sample is selected by choosing every kth element after randomly selecting the first element. Area sampling involves dividing a population into non-overlapping regions and randomly selecting regions to sample from. Stratified sampling involves dividing a population into homogeneous subgroups (strata) and then randomly selecting individuals from each subgroup. Stratified simple random sampling involves randomly selecting individuals from each subgroup in proportion to their size. The description of the sampling method in the question matches the definition of systematic sampling.

Question 19

The advantage of nonprobabilistic sampling is that it is inexpensive and

Accepted Answer

Nonprobabilistic sampling is not based on random selection, therefore it cannot provide statistically valid statements about the precision of the estimate or valid parameter estimates. Additionally, nonprobabilistic sampling is not error-free and can introduce bias into the results. Therefore, none of the alternatives are correct.

Question 20

Errors such as measurement error, processing error, and interviewer error are

Accepted Answer

Measurement error, processing error, and interviewer error are considered nonsampling errors because they occur due to factors other than the sampling process. Sampling errors, on the other hand, occur due to chance variations in the selection of the sample. It is important to address both types of errors in order to ensure accurate results in statistical analysis.

Quiz 21: Sample Survey

Exhibit 21-4 Simple random sampling has been used to obtain a sample of size 50 from a population of size 500. The sample proportion was 0.7. -Refer to Exhibit 21-4. The estimate of the standard error of proportion is

Exhibit 21-3 From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40. -Refer to Exhibit 21-3. An approximate 95% confidence interval for the population mean is

Exhibit 21-3 From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40. -Refer to Exhibit 21-3. An estimate of the standard error of the mean is

An unbiased estimate of the population total is given by the

With nonprobabilistic sampling

A version of cluster sampling in which the elements are formed into clusters on the basis of their geographic proximity is

Exhibit 21-2 A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60. -Refer to Exhibit 21-2. An approximate 95% confidence interval for the population mean is

Exhibit 21-1 A simple random sample of size 64 is taken from a population of size 800. The sample mean is determined to be 2,550 with a standard deviation of 500. -Refer to Exhibit 21-1. The point estimate of the population total is

Exhibit 21-3 From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40. -Refer to Exhibit 21-3. An approximate 95% confidence interval for the population total is

Exhibit 21-2 A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60. -Refer to Exhibit 21-2. An approximate 95% confidence interval for the population total is

Exhibit 21-3 From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40. -Refer to Exhibit 21-3. The population total is

Sampling errors can

Exhibit 21-2 A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60. -Refer to Exhibit 21-2. The standard error of the mean is

Which of the following is (are) the most common type(s) of surveys?

Exhibit 21-1 A simple random sample of size 64 is taken from a population of size 800. The sample mean is determined to be 2,550 with a standard deviation of 500. -Refer to Exhibit 21-1. An estimate of the standard error of the mean (for the total) is

Exhibit 21-2 A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60. -Refer to Exhibit 21-2. The population total is

In a sample survey, it is common practice to use a t value of (when approximating a 95% confidence interval)

A method of selecting a sample by randomly selecting the first element and then selecting every kth element thereafter is

The advantage of nonprobabilistic sampling is that it is inexpensive and

Errors such as measurement error, processing error, and interviewer error are

A method of selecting a sample by randomly selecting the first element and then selecting every k^th element thereafter is