Question 1

Which of the following best describes the purpose of calculating a z-score for a data point?

Accepted Answer

To standardize the data point by measuring its distance from the mean in units of standard deviation.

Question 2

Given a data set with mean $$\bar{y} = 50$$ and standard deviation $$s = 10$$, what is the z-score for a value $$y = 70$$?

Accepted Answer

$$z = \frac{70 - 50}{10} = 2$$

Question 3

Which property is NOT changed when data is standardized into z-scores?

Accepted Answer

The shape of the distribution.

Question 4

A normal model is defined by which two parameters?

Accepted Answer

Mean ($$\mu) $$and standard deviation ($$\sigma)$$

Question 5

In a normal distribution, what percentage of values fall within one standard deviation of the mean?

Accepted Answer

68%

Question 6

Which of the following is a requirement for a density curve?

Accepted Answer

The total area under the curve must equal 1.

Question 7

A normal probability plot is used to:

Accepted Answer

Check if the data follows a normal distribution.

Question 8

If a normal probability plot shows points curving up and to the left, what does this indicate about the data?

Accepted Answer

The data is right-skewed.

Question 9

Which sampling method involves dividing the population into homogenous groups and then sampling from each group?

Accepted Answer

Stratified sampling

Question 10

What is the main advantage of randomizing when selecting a sample?

Accepted Answer

It protects against both known and unknown sources of bias.

Question 11

Which of the following is an example of response bias in a survey?

Accepted Answer

Using a question wording that influences how people answer.

Question 12

A researcher wants to estimate the average height of students at a university. She randomly selects 5 dorms and surveys all students in those dorms. Which sampling method is she using?

Accepted Answer

Cluster sampling

Question 13

Which of the following statements about sample size is correct?

Accepted Answer

A larger sample size increases the likelihood of the sample being representative.

Question 14

What is the formula for calculating a z-score?

Accepted Answer

$$z = \frac{y - \bar{y}}{s}$$

Question 15

Which of the following is NOT a common mistake in sampling?

Accepted Answer

Randomizing the selection process.

Question 16

In the context of survey sampling, what is undercoverage?

Accepted Answer

Excluding certain groups from the sampling frame, leading to bias.

Question 17

Which notation is typically used for the population mean?

Accepted Answer

$$\mu$$

Question 18

A survey is conducted by selecting every 10th person from a list after starting at a random number. What sampling method is this?

Accepted Answer

Systematic sampling

Question 19

If a sample statistic accurately reflects the corresponding population parameter, the sample is said to be:

Accepted Answer

Representative

Question 20

Which of the following best describes the 68-95-99.7 rule in a normal distribution?

Accepted Answer

68% of values fall within one standard deviation, 95% within two, and 99.7% within three standard deviations of the mean.

Standardization, Normal Models, and Sampling in Statistics

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