Q: A researcher surveys 200 people and finds that 120 prefer Brand A. The population proportion is believed to be $p = 0.5$. What is the standard error of the proportion?

$\sigma_{\hat{p}} = \sqrt{\frac{0.5 \times 0.5}{200}} = 0.0354$

Question 1

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

Accepted Answer

The CLT states that 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 20 employees from a company of 400 using systematic sampling. What is the value of $k$ (the sampling interval) that should be used?

Accepted Answer

$k = \frac{400}{20} = 20$

Question 3

Which of the following is an example of undercoverage bias?

Accepted Answer

A survey about campus facilities is sent only to students living on campus, excluding those who commute.

Question 4

A sample of 100 customers is drawn from a population of 1,000. The population standard deviation is $\sigma = 20$. What is the standard error of the mean?

Accepted Answer

$\sigma_{\bar{x}} = \frac{20}{\sqrt{100}} = 2$

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 claims that 80% of its products pass quality control. In a random sample of 50 products, 35 pass. What is the sample proportion $\hat{p}$?

Accepted Answer

$\hat{p} = \frac{35}{50} = 0.70$

Question 7

Which of the following is a key disadvantage of systematic sampling?

Accepted Answer

It can be affected by periodicity in the population, leading to biased samples.

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

Which of the following best describes a convenience sample?

Accepted Answer

A sample where members are chosen because they are easily accessible.

Question 10

A researcher surveys 200 people and finds that 120 prefer Brand A. The population proportion is believed to be $p = 0.5$. What is the standard error of the proportion?

Accepted Answer

$\sigma_{\hat{p}} = \sqrt{\frac{0.5 	imes 0.5}{200}} = 0.0354$

Question 11

Which of the following is an example of confirmation bias?

Accepted Answer

A manager only pays attention to sales data that supports her belief that a new product is successful, ignoring data that suggests otherwise.

Question 12

Which formula is used to calculate the standard error of the mean when sampling from a finite population?

Accepted Answer

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

Question 13

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

Accepted Answer

Availability heuristic bias

Question 14

Which of the following statements about the mean of the sample means is correct according to the Central Limit Theorem?

Accepted Answer

The mean of the sample means is equal to the population mean.

Question 15

A sample of size $n = 40$ is drawn from a population of $N = 100$ with $\sigma = 0.7$. What is the finite population correction factor?

Accepted Answer

$\sqrt{\frac{100-40}{100-1}} = \sqrt{\frac{60}{99}} \approx 0.777$

Question 16

Which of the following is NOT a probability sampling method?

Accepted Answer

Convenience sampling

Question 17

A researcher wants to estimate the proportion of defective items in a large shipment. Which condition must be met to use the normal approximation for the sampling distribution of the proportion?

Accepted Answer

$np \geq 5$ and $nq \geq 5$

Question 18

Which of the following is an example of voluntary response bias?

Accepted Answer

A radio show asks listeners to call in and share their opinions, and only those with strong feelings respond.

Question 19

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.

Sampling and Sampling Distributions – Study Notes

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