Deck 13: Inference Without Normality

Question 1

A new fiber bar is advertised to curb hunger for three hours. A sample of fourteen hungry subjects was asked to record their level of hunger before eating the fiber bar and again three hours after eating the fiber bar. Which of the following is a better method for testing whether there is a difference in the level of hunger three hours after eating the fiber bar (i.e. the fiber bar curbed hunger for three hours)?

A)Data transformation and t-confidence interval of transformed data
B)Paired t-test
C)Sign Test
D)Mann-Whitney Test

Answer 1

Sign Test

Question 2

Which of the following is an indication that nonparametric inference might be necessary?

A)The sample size is too large to assume the CLT holds.
B)The distribution of the population is strongly skewed.
C)The distribution of the population is Normal.
D)The sample standard deviation is smaller than the sample mean.

Answer 2

The distribution of the population is strongly skewed.

Question 3

Explain some features of the data that might indicate that nonparametric inference might be useful.

Answer 3

Sample size is small, the population is not normal, the data is strongly skewed.

Question 4

In the context of nonparametric inference, what information can the QQ plot provide?

A)It is a tool that displays quartile locations of data values which can provide information about the sample distribution.
B)It is tool that displays the distribution of transformed data.
C)It is a tool that can help you determine whether a sample is drawn from a normal population.
D)None of the above

Question 5

Which of the following statements is not true about the sign test?

A)Matched pairs must be independent of other pairs in the sample.
B)The sign test relies on the signs (negative or positive) of the measured differences in pairs.
C)The p-value is based on the normal distribution.
D)The binomial model is used to find an exact p-value.

Question 6

Which of the following statements is not true about the sign test for paired data?

A)The sign test is a nonparametric test that can be used in place of the paired t-test.
B)The sign test is a nonparametric test based on the median of a population.
C)The sign test is similar to the paired t-test in that both are based on examining differences between paired observations.
D)The sign test is a nonparametric test based on the mean of a population.

Question 7

A used car lot owner wanted to estimate the amount spent by customers during the summer months. She took a random sample of customers and recorded the amount they spent. A histogram showed the data was right-skewed so she took the log of each value and verified that the distribution of these values was more normally distributed. What test/method should she use to estimate the mean amount spent during the summer months?

A)Data transformation
B)Paired t-test
C)Sign Test
D)Mann-Whitney Test

Question 8

Describe some features of the data that might indicate that sign test would be useful for inference.

Question 9

You are presented with data from two independent samples. The variable being measured is continuous. The distribution of the population of each sample is right skewed. You wish to test the hypothesis that there is a difference in the median value of the variable for the samples. Which of the following is the better method for testing whether the medians differ?

A)Data transformation and t-confidence interval of transformed data
B)Paired t-test
C)Sign Test
D)Mann-Whitney Test

Question 10

Which of the following is not necessarily an indication that nonparametric inference might be necessary?

A)Observations are be matched pairs
B)The sample size is too small to assume the CLT holds.
C)The distribution of the population is not Normal.
D)The distribution of the sample is strongly skewed

Question 11

You are presented with data from two independent samples. The variable being measured is numerical and continuous-valued. The distribution of the population of each sample is right skewed. You wish to test the hypothesis that there is a difference in the median value of the variable for the samples. What type of test/method should you use? Explain why the t-test is not the best method in this situation.

Question 12

Choose the statement that is not true about the Mann-Whitney Test.

A)The Mann-Whitney Test is based on the number of pairs with negative differences.
B)The Mann-Whitney Test can be used when the Normal condition of the t-test is not met.
C)The Mann-Whitney Test is based on the ranks of the observations, not on their actual values.
D)The Mann-Whitney Test is used to compare the centers of two groups of numerical variables.

Question 13

Suppose data were collected from ten women and twelve men about the length in minutes of their commute to work. The histogram for men was roughly normal, but the histogram for women was strongly skewed to the right. Explain why the t-test is not the best test of whether men and women have different typical commute times.

Question 14

Which of the following presents, in this order, the mean, median, and geometric mean of these numbers: 400, 120, 1300, and 22000. Round to the nearest tenth.

A)5955.0, 850.0, 1185.5
B)5955.0, 710.0, 1082.4
C)5955.0, 710.0, 1185.5
D)5955.0, 850.0, 1082.4

Question 15

In the context of nonparametric inference, what information can the QQ plot provide?

A)It is a tool that can be used to determine if the mean and median are equal to each other.
B)It is a tool that can be used to determine if the standard deviation is normally distributed.
C)It is a tool that can be used to determine whether a sample is drawn from a uniform distribution.
D)It is a tool that can be used to determine whether a sample is drawn from a normal population.

Question 16

Which of the following statements could be a reason to justify the use of the sign test?

A)The data are matched pairs
B)The sample size is small
C)The distribution of the population is unknown or not Normal
D)All of the above

Question 17

Calculate the mean, median, and geometric mean for the following numbers: 710, 27,000, 1400, and 260. Round to the nearest tenth.

Question 18

List three of the five conditions, pertaining to the sample, which must be met in order to use the Mann-Whitney test.

Question 19

Suppose you are asked to analyze sample data but you do not know the distribution of the population it came from. Explain how a QQ plot can be used to give you information about the population from which the samples was drawn.

Question 20

Which of the following presents, in this order, the mean, median, and geometric mean of these numbers: 410, 20, 1750, 66000. Round to the nearest tenth.

A)17045.0, 885.0, 986.5
B)17045.0, 885.0, 3.0
C)17045.0, 1080.0, 3.0
D)17045.0, 1080.0, 986.5

Question 21

Which of the following conditions is not a requirement for the Mann-Whitney Test?

A)The population distributions of the groups have the same shape.
B)The response variable must be numerical and continuous.
C)There are two independent groups.
D)There are two paired groups.

Question 22

Which of the following statements is true about the sign test for paired data?

A)The sign test relies only on the signs of the differences in pairs, not the values of the differences.
B)The sign test relies only on the values of the differences in pairs, not the signs of the differences.
C)The sign test is a nonparametric test because it makes two assumptions about the distributions of the populations.
D)The sign test is most useful if you know your data are normally distributed.

Question 23

A soccer fan was interested in estimating the mean salary of professional soccer players. He took a random sample of professional soccer players and recorded the annual salaries of each. After looking at a histogram of the data, he noticed that the data were right-skewed. He took the log of each value and verified that the distribution of these transformed data was approximately normal. What test/method should be used to estimate the mean annual salary of profession soccer players?

A)Sign test
B)Data transformation and t-confidence interval of transformed data
C)Mann-Whitney Test
D)Independent samples t-test

Question 24

Do daughters tend to be taller than their mothers? To answer this question, the heights of mothers and daughters from 20 families were recorded. Which of the following is the better method for testing whether daughters tend to be taller than mothers?

A)Sign test
B)Data transformation and t-confidence interval of transformed data
C)Mann-Whitney Test
D)Independent samples t-test

Question 25

Are price/earnings ratios typically different for firms in the energy equipment sector and firms in the hotel, restaurant and leisure sector? To answer this question, 15 firms in each sector are randomly selected and the price/earnings ratios recorded for each. Which of the following is the better method for testing whether the sectors typically differ in price/earnings ratio?

A)Sign test
B)Data transformation and t-confidence interval of transformed data
C)Mann-Whitney Test
D)Independent samples t-test