Exam 13: Inference Without Normality

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?

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

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?

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.

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?

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 is an indication that nonparametric inference might be necessary?

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

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

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.

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?

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

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

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

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.

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

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

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)?

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