Question 1

Which of the following best describes a simple random sample from a finite population?

Accepted Answer

A sample in which every element has an equal chance of being selected, and each possible sample of a given size has an equal chance of being chosen.

Question 2

A company wants to estimate the average salary of its employees. They select 50 employees at random from a list of 500. What is the expected value of the sample mean $$\bar{x}$$?

Accepted Answer

$$E(\bar{x}) = \mu$$

Question 3

Which formula gives the standard deviation of the sample mean $$\bar{x}$$ for a simple random sample from a finite population?

Accepted Answer

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

Question 4

According to the Central Limit Theorem, as the sample size $$n$$ increases, the sampling distribution of the sample mean $$\bar{x}$$:

Accepted Answer

Approaches a normal distribution, regardless of the shape of the population distribution.

Question 5

A researcher selects every 10th person from a list of 1,000 customers. Which sampling method is being used?

Accepted Answer

Systematic sampling

Question 6

Which of the following is a key advantage of stratified random sampling over simple random sampling?

Accepted Answer

It ensures representation from all subgroups of the population.

Question 7

If a sample is selected with replacement from an infinite population, which condition must be satisfied for the sample to be considered random?

Accepted Answer

Each element selected comes from the population and each element is selected independently.

Question 8

A business analyst wants to estimate the proportion of customers who prefer online shopping. She randomly selects 200 customers and finds that 120 prefer online shopping. What is the point estimate for the population proportion $$p$$?

Accepted Answer

$$\hat{p} = \frac{120}{200} = 0.6$$

Question 9

Which formula is used to calculate the standard deviation of the sample proportion $$\hat{p}$$ for a simple random sample from a finite population?

Accepted Answer

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

Question 10

A company divides its employees into departments and randomly selects some departments, then surveys all employees in those departments. Which sampling method is this?

Accepted Answer

Cluster sampling

Question 11

Why is convenience sampling generally discouraged in business research?

Accepted Answer

It may lead to biased results because the sample may not be representative of the population.

Question 12

If the population standard deviation $$\sigma is 20 $$and the sample size $$n is 25$$, what is the standard deviation of the sample mean $$\bar{x}$$ for an infinite population?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{20}{\sqrt{25}} = 4$$

Question 13

Which of the following statements about the relationship between sample size and the standard deviation of the sample mean $$\bar{x} is $$correct?

Accepted Answer

As the sample size increases, the standard deviation of $$\bar{x}$$ decreases.

Question 14

A market researcher uses judgment sampling to select participants for a survey. What is a potential drawback of this method?

Accepted Answer

The sample may reflect the researcher's biases and not be representative of the population.

Question 15

A sample of 100 employees is taken from a population of 1,000. The population mean salary is $$\50$$,000$$ and the population standard deviation is $$\$$8,000. $$What is the standard deviation of the sample mean $$\bar{x}$$ for a finite population?

Accepted Answer

$$\sigma_{\bar{x}} = \sqrt{\frac{1000-100}{999}} \cdot \frac{8000}{\sqrt{100}}$$

Question 16

Which of the following is NOT a probability sampling method?

Accepted Answer

Convenience sampling

Question 17

A sample proportion $$\hat{p} is $$used to estimate the population proportion $$p. $$What is the expected value of $$\hat{p}$$?

Accepted Answer

$$E(\hat{p}) = p$$

Question 18

A company wants to estimate the average number of sick days taken by employees. They select a simple random sample of 40 employees from a population of 400. Which sampling method is being used?

Accepted Answer

Simple random sampling

Question 19

Which of the following best describes the practical value of the sampling distribution of $$\bar{x}$$?

Accepted Answer

It allows us to determine the probability that a sample mean falls within a specified range of the population mean.

Sampling and Sampling Distributions: Study Notes for Statistics for Business

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