Question 1

Which of the following best describes the Central Limit Theorem (CLT)?

Accepted Answer

The sample means of large-sized samples will be normally distributed regardless of the shape of their population distributions.

Question 2

A researcher wants to select a sample of 10 students from a population of 1,800 students using systematic sampling. What is the value of k (the sampling interval) that should be used?

Accepted Answer

$$k = \frac{N}{n} = \frac{1800}{10} = 180$$

Question 3

Which of the following is an example of undercoverage bias?

Accepted Answer

A survey about campus dining is sent only to students living in dorms, excluding those who live off-campus.

Question 4

Given a population with mean $$\mu = 15$$ and standard deviation $$\sigma = 2.24$$, what is the standard error of the mean for samples of size $$n = 2$$?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{2.24}{\sqrt{2}} = 1.58$$

Question 5

Which sampling method divides the population into mutually exclusive groups and then randomly samples from each group?

Accepted Answer

Stratified sampling

Question 6

A company surveys 40 out of its 100 customers and finds a sample mean rating of 7.5. The population mean is 7.2 with a standard deviation of 0.7. What formula should be used to calculate the standard error of the mean in this finite population scenario?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \sqrt{\frac{N-n}{N-1}}$$

Question 7

Which of the following is a nonprobability sampling method?

Accepted Answer

Convenience sampling

Question 8

If a sample statistic is not likely to be exactly equal to the population parameter, what is this difference called?

Accepted Answer

Sampling error

Question 9

A survey asks respondents to recall how many times they visited a store in the past year. Which bias is most likely to affect the results?

Accepted Answer

Availability heuristic bias

Question 10

A sample proportion is calculated as $$\hat{p} = \frac{x}{n}. In a $$survey of 120 students, 97 found jobs related to their major. What is the sample proportion?

Accepted Answer

$$\hat{p} = \frac{97}{120} = 0.808$$

Question 11

Which of the following statements about cluster sampling is correct?

Accepted Answer

Clusters are mini-subsets of the population and tend to be heterogeneous within each cluster.

Question 12

Which formula is used to calculate the standard error of the proportion?

Accepted Answer

$$\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$$

Question 13

A researcher calculates a z-score for a sample mean using $$z = \frac{\bar{x} - \mu_{\bar{x}}}{\sigma_{\bar{x}}}. If$$ $$\bar{x} = 45$$, $$\mu_{\bar{x}} = 50$$, and $$\sigma_{\bar{x}} = 2.16$$, what is the z-score?

Accepted Answer

$$z = \frac{45 - 50}{2.16} = -2.31$$

Question 14

Which of the following is a key advantage of probability sampling over nonprobability sampling?

Accepted Answer

Probability sampling allows for inferential statistical tests to draw reliable conclusions about the population.

Question 15

Which type of bias occurs when survey respondents provide inaccurate answers due to leading questions?

Accepted Answer

Response bias

Question 16

If the sample size increases while the population standard deviation remains constant, what happens to the standard error of the mean?

Accepted Answer

It decreases.

Question 17

Which of the following is a correct interpretation of the Central Limit Theorem for sample sizes of 30 or more?

Accepted Answer

The distribution of sample means will be approximately normal regardless of the population's distribution.

Question 18

A survey is sent out, but only those with strong opinions respond. What type of bias is most likely present?

Accepted Answer

Voluntary response bias

Sampling and Sampling Distributions: Core Concepts and Applications

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