Question 1

Which of the following best explains why sampling is often preferred over studying an entire population in business statistics?

Accepted Answer

Sampling is less expensive, less time-consuming, and can be more practical, especially when tests are destructive or the population is very large.

Question 2

A company wants to estimate the average lifetime of its light bulbs. Testing every bulb would destroy the entire inventory. Which reason for sampling does this scenario best illustrate?

Accepted Answer

Sampling is necessary due to the destructive nature of the test.

Question 3

Which of the following is a probability sampling method where the population is divided into mutually exclusive groups and a random sample is taken from each group?

Accepted Answer

Stratified random sampling

Question 4

In systematic random sampling, how is the value of $$k ($$the sampling interval) determined?

Accepted Answer

$$k = N / n$$

Question 5

Which type of error is introduced when certain groups in the population are not adequately represented in the sample?

Accepted Answer

Coverage error (selection bias)

Question 6

A survey is sent to 1,000 customers, but only 200 respond. Which type of error is most likely present?

Accepted Answer

No response error

Question 7

Which formula gives the standard error of the sample mean for a population with standard deviation $$\sigma$$ and sample size $$n$$?

Accepted Answer

$$\sigma_x = \frac{\sigma}{\sqrt{n}}$$

Question 8

According to the Central Limit Theorem, as the sample size $$n$$ increases, the sampling distribution of the sample mean:

Accepted Answer

Becomes approximately normal regardless of the population distribution.

Question 9

Refer to the image provided. As the sample size increases from $$n=2 to$$ $$n=30$$, what happens to the shape of the sampling distribution of the sample mean for a right-skewed population?

Accepted Answer

It becomes more symmetric and approaches a normal distribution.

Question 10

Which formula should be used to calculate the z-score for a sample mean when sampling from a finite population without replacement?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \sqrt{\frac{N-n}{N-1}}$$

Question 11

A sample proportion $$\hat{p} is $$calculated from a sample of size $$n. $$What is the standard error of $$\hat{p}$$?

Accepted Answer

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

Question 12

Which of the following is NOT a requirement for the Central Limit Theorem to apply to sample proportions?

Accepted Answer

Population must be normally distributed.

Question 13

If a sample is not representative of the population due to poor sampling technique, which type of error is most likely present?

Accepted Answer

Non-sampling error (bias)

Question 14

Which of the following best describes a point estimate?

Accepted Answer

A single value calculated from a sample used to estimate a population parameter.

Question 15

A researcher divides a city into neighborhoods and randomly selects several neighborhoods to survey all households within them. Which sampling method is this?

Accepted Answer

Cluster sampling

Question 16

Which formula gives the finite population correction factor for the standard error of the mean?

Accepted Answer

$$\sqrt{\frac{N-n}{N-1}}$$

Question 17

If the population mean is $$\mu = 50$$, the population standard deviation is $$\sigma = 10$$, and a sample of size $$n = 25 is $$taken, what is the standard error of the mean?

Accepted Answer

$$2$$

Question 18

Which of the following is an example of a non-probability sampling method?

Accepted Answer

Convenience sampling

Question 19

A survey question is worded ambiguously, leading respondents to interpret it differently. Which type of error does this introduce?

Accepted Answer

Measurement error

Question 20

Which formula is used to calculate the z-score for a sample proportion?

Accepted Answer

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

Sampling and Sampling Distributions: Concepts, Methods, and Applications

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