Question 1

Which of the following best describes what a z-score represents in a data set?

Accepted Answer

The number of standard deviations a value is from the mean.

Question 2

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

Accepted Answer

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

Question 3

Which of the following is NOT a property of the normal model $$\mathcal{N}(\mu, \sigma)$$?

Accepted Answer

It is always skewed to the right.

Question 4

A researcher wants to estimate the average height of all university students. Which sampling method would best ensure that students from all majors are represented?

Accepted Answer

Stratified sampling

Question 5

What does the 68-95-99.7 rule state about data in a normal distribution?

Accepted Answer

About 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.

Question 6

Which of the following is a potential source of bias in survey sampling?

Accepted Answer

Only sampling volunteers

Question 7

If a normal probability plot shows a strong curve upward and to the left, what does this indicate about the data?

Accepted Answer

The data is right-skewed.

Question 8

Which of the following statements about density curves is FALSE?

Accepted Answer

The area under a density curve can be greater than 1.

Question 9

A sample statistic is said to be representative if:

Accepted Answer

It accurately reflects the corresponding population parameter.

Question 10

Which of the following best describes the effect of standardizing data into z-scores?

Accepted Answer

It shifts the mean to 0 and rescales the standard deviation to 1.

Question 11

A hospital wants to estimate the average recovery time for a new treatment. They divide patients into age groups and randomly sample from each group. What sampling method is this?

Accepted Answer

Stratified sampling

Question 12

Which of the following is an example of undercoverage bias?

Accepted Answer

Excluding homeless individuals from a housing survey.

Question 13

If a sample is selected by choosing every 10th person from a list after a random start, what type of sampling is this?

Accepted Answer

Systematic sampling

Question 14

Which of the following is a key difference between stratified and cluster sampling?

Accepted Answer

Stratified sampling samples from every group, while cluster sampling samples entire groups.

Question 15

A researcher calculates a z-score of $$-1.5$$ for a test score. What does this indicate?

Accepted Answer

The score is 1.5 standard deviations below the mean.

Question 16

Which of the following is NOT a step in calculating a z-score?

Accepted Answer

Multiply the mean by the standard deviation.

Question 17

Why is randomization important in sample surveys?

Accepted Answer

It protects against both known and unknown sources of bias.

Question 18

Which of the following best describes a population parameter?

Accepted Answer

A numerical value that describes a characteristic of the entire population.

Question 19

A normal model is described by $$\mathcal{N}(\mu, \sigma). $$What do $$\mu$$ and $$\sigma$$ represent?

Accepted Answer

$$\mu is $$the mean and $$\sigma is $$the standard deviation.

Question 20

Which of the following is a valid reason why a census is often not feasible?

Accepted Answer

It is difficult to reach every individual in the population.

Z-Scores, Normal Models, and Sampling in Statistics

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