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)?

Accepted Answer

C

Question 2

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

Accepted Answer

Nonparametric inference is often necessary when the population distribution is not normal, such as when it is strongly skewed. This is because nonparametric methods do not assume a specific distribution shape, making them suitable for analyzing data that do not meet the assumptions of parametric tests, like normality.

Question 3

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

Accepted Answer

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?

Accepted Answer

A QQ plot, or quantile-quantile plot, is a graphical tool used to compare the quantiles of a sample distribution to the quantiles of a theoretical distribution, often the normal distribution. It is particularly useful for assessing if a sample comes from a normally distributed population.

Question 5

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

Accepted Answer

The sign test does not rely on the normal distribution for calculating the p-value; instead, it uses the binomial distribution to determine the exact p-value.

Question 6

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

Accepted Answer

The sign test is a nonparametric test that does not make assumptions about the population distribution and is based on the median of the differences between paired observations, not the mean.

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?

Accepted Answer

Data transformation has already been applied by taking the log of each value to normalize the distribution, allowing for parametric tests to estimate the mean.

Question 8

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

Accepted Answer

The answer of Describe some features of the data that...

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?

Accepted Answer

The Mann-Whitney Test is a non-parametric test that is suitable for comparing medians between two independent samples, especially when the data is not normally distributed, as is the case with right-skewed distributions.

Question 10

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

Accepted Answer

Nonparametric inference is not necessarily required for matched pairs alone; it depends more on the distribution of the data and the size of the sample rather than the pairing of observations. Matched pairs can be analyzed using parametric methods if the differences between pairs are normally distributed or if the sample size is large enough for the Central Limit Theorem to apply.

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.

Accepted Answer

The answer of You are presented with data from two...

Question 12

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

Accepted Answer

The Mann-Whitney Test is not based on the number of pairs with negative differences; instead, it ranks all the observations from both groups together and then compares the ranks between the two groups.

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.

Accepted Answer

The answer of Suppose data were collected from ten women...

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.

Accepted Answer

The answer of Which of the following presents, in this...

Question 15

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

Accepted Answer

The QQ (quantile-quantile) plot is a graphical tool used to compare the quantiles of a sample distribution to the quantiles of a theoretical distribution, often the normal distribution. It helps in assessing if the sample data comes from a specified distribution, such as a normal distribution.

Question 16

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

Accepted Answer

The sign test can be justified for use when the data are matched pairs, when the sample size is small, and when the distribution of the population is unknown or not normal, making all of the provided options valid reasons.

Question 17

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

Accepted Answer

The answer of Calculate the mean, median, and geometric mean...

Question 18

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

Accepted Answer

The answer of List three of the five conditions, pertaining...

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.

Accepted Answer

The answer of Suppose you are asked to analyze sample...

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.

Accepted Answer

The answer of Which of the following presents, in this...

Quiz 13: Inference Without Normality

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

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

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

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

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

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

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

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

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.

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

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

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

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

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.

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.