Question 1

Which of the following is the best initial step to assess whether a sample of data comes from a population with a normal distribution?

Accepted Answer

Construct a histogram and check if it is roughly bell-shaped.

Question 2

A normal quantile plot (or normal probability plot) is used to:

Accepted Answer

Graph the original data values against their expected z-scores from the standard normal distribution.

Question 3

Which of the following patterns in a normal quantile plot suggests that the data are NOT from a normal distribution?

Accepted Answer

The points show a systematic curve away from a straight line.

Question 4

Suppose you have a histogram of IQ scores that is roughly bell-shaped and a normal quantile plot where the points are close to a straight line. What is the most reasonable conclusion?

Accepted Answer

The data are likely from a population with a normal distribution.

Question 5

Which of the following is NOT a formal test for normality?

Accepted Answer

Chi-square test for independence

Question 6

If a histogram of data is skewed to the right and the normal quantile plot shows points far from a straight line, what should you conclude?

Accepted Answer

The data are not from a normal distribution.

Question 7

Which of the following statements about outliers is TRUE?

Accepted Answer

Outliers may reveal important information and should only be discarded if they are errors.

Question 8

A data set is not normally distributed. Which transformation is commonly used to attempt to normalize the data?

Accepted Answer

Take the logarithm of each value.

Question 9

If the distribution of the logarithms of a data set is normal, what is the distribution of the original data called?

Accepted Answer

Lognormal distribution

Question 10

The Ryan-Joiner test for normality is based on:

Accepted Answer

The correlation between the data and the normal scores.

Question 11

A Dallas commute time data set has a histogram that is skewed to the left and a normal quantile plot with points far from a straight line. What is the best conclusion?

Accepted Answer

The data are not from a normal distribution.

Question 12

Which of the following is a correct procedure for assessing normality in a data set?

Accepted Answer

Construct a histogram and, if it is roughly bell-shaped, construct a normal quantile plot.

Question 13

Which of the following is a sign that a normal quantile plot indicates a non-normal distribution?

Accepted Answer

The points show a systematic S-shaped curve.

Question 14

If a data set contains outliers, what is the recommended approach?

Accepted Answer

Analyze the data both with and without the outliers to assess their impact.

Question 15

Which of the following tests is NOT specifically designed to assess normality?

Accepted Answer

ANOVA F-test

Question 16

A normal quantile plot is constructed by plotting:

Accepted Answer

Sample data values against their expected normal z-scores.

Question 17

Which of the following is a reason to transform data using logarithms?

Accepted Answer

To make a skewed distribution more normal.

Question 18

If a normality test returns a p-value greater than 0.10, what is the most appropriate conclusion?

Accepted Answer

Fail to reject the null hypothesis; the data are likely normal.

Question 19

Which of the following is a correct interpretation of a histogram that is flat (uniform) and a normal quantile plot that shows a systematic pattern not close to a straight line?

Accepted Answer

The data are from a uniform distribution, not normal.

Question 20

Which of the following is a multi-step approach to assess normality in a real-world scenario, such as analyzing rainfall data?

Accepted Answer

Construct a histogram, check for bell shape, then construct a normal quantile plot and check for a straight-line pattern.

6.5 Assessing Normality in Normal Probability Distributions

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