Exam 13: Nonparametric Statistics

If a variable is normally distributed, researchers will need more data to determine the same information using parametric methods than they would using nonparametric methods. In other words, parametric methods are not as efficient as nonparametric methods.

For a specific year, the median price of natural gas was $\$ 11.99$ per 1000 cubic feet. A researcher wishes to see if there is enough evidence to reject the claim. Out of 43 households, 34 paid less than $\$ 11.99$ per 1000 cubic feet for natural gas. Test the claim at $\alpha = 0.05$ .

Six second grade students tried tossing a ball into a basket ten times each. Their teacher tl suggested a different way of tossing the ball, and the six students tried again. The numbe successful tosses, before and after the teacher's added instruction, are shown below. Student Before the suggestion (out of 10) 6 5 6 2 6 5 After the suggestion (out of 10) 2 5 2 4 2 5 Find the signed rank of child A's difference. [Recall, differences of zero are not ranked.]

Six second-graders tried tossing a ball into a basket ten times each. Their teacher then sug a different way of tossing the ball, and the six students tried again. The number of succes tosses, before and after the teacher's suggestion, are shown below. Student Before the suggestion (out of 10) 2 3 7 2 7 3 After the suggestion (out of 10) 3 3 5 3 5 3 Find the sum of the positive and negative rank sums as in a Wilcoxon signed-rank test. gested

Two students rated, then ranked six different television shows. The final rankings are listed in the table below. Compute the Spearman rank correlation coefficient $r _ { s }$ for their rankings. Show Student 1 1 6 3 4 2 5 Student 2 3 6 1 5 4 2

What is another term for nonparametric statistics?

A professional golfer wanted to determine if there was a difference in the number of yards that golfers could hit a ball depending on the brand of driver (a particular type of club) used. Twenty-five golfers (of approximately the same ability) were divided into five groups ,and each golfer in a group hit a ball with one particular brand of driver. The number of yards they hit the ball was recorded, and a rank was assigned to each value. The data are tabulated below with the number of yards hit listed first and the ranks listed in parentheses. Brand A Brand B Brand C Brand D Brand E 300(25) 190(5) 235(11) 275(17) 165(2) 298(23) 164(1) 296(21) 299(24) 175(3) 297(22) 239(13) 274(16) 185(4) 256(14) 260(15) 215(7) 280(18) 238(12) 224(9) 295(20) 225(10) 290(19) 196(6) 219(8) Compute the appropriate test value for a Kruskal-Wallis test, at $\alpha = 0.05$ , of the professio golfer's hypothesis. onal

Men and women were randomly selected to rate eight television programs on a scale of 1 to 50 with 50 being the best score. The average ratings are shown in the table below. Use the Spearman rank correlation coefficient at $\alpha = 0.05$ to determine if there is a correlation between the rankings of men and women. Program A B C D E F G H Men 32 50 6 15 29 48 36 10 Women 20 48 10 25 37 50 29 16

Nonparametric methods tend to use less information than their parametric counterparts.

Two students were asked to rate six different television shows on a scale from 1 to 10 points, with higher values ranking ahead of lower values. The data are shown in the follor table: Show Student 1 2 8 6 4 9 7 Student 2 7 9 3 4 2 5 Which table shows the appropriate differences in the rankings needed in the computation the Spearman rank correlation coefficient?

A landscaping company hypothesizes that the median number of lawns they mow in a we 20. They tabulated the number of lawns mowed in a random sample of 14 weekends. 22 18 19 20 25 20 18 22 23 20 21 26 24 22 What critical value should be used for this two-tailed test at $\alpha = 0.10$ ? d is

The following data was collected as part of a study examining whether there is a difference between the number of hours men and women watch television. The values represent the number of hours a subject watched television on a designated Monday night. In the process of computing the test value the data from both samples should be combined, arranged in order, and ranked according to each group. Calculate the sum of th for both groups. Lower values rank ahead of higher ones. Men 2.0 1.5 3.0 2.5 2.0 1.0 0.0 2.0 1.5 2.5 2.0 2.0 Women 2.0 2.5 1.0 1.0 1.5 2.5 2.0 1.0 2.0 1.5 1.0 0.0

If a researcher is using the sign test and has 3 positive signs, 8 negative signs, and 4 zeros, what is the test value?

Which of the following is not an advantage of nonparametric methods over parametric methods?

The is used to test a hypothesis about a median value for a sample. It includes counting the number of values greater or less than the hypothesized median value.

Many nonparametric tests involve , which is the same as positioning the data values in a data array according to some scale.

In the Wilcoxon rank sum test, if the hypothesis is true, the values in the different groups will not be ranked similarly.

Given the following data set, what is the ranking of the data value 15? Presume that lowerdata values rank ahead of higher data values. 16, 18, 12, 19, 15, 20, 13, 18

Given the following data set, what is the ranking of the data value 28? Presume that lower data values rank ahead of higher data values. 31, 28, 21, 27, 38, 33, 16, 28

Two independent sets of data are collected, the first with 15 subjects and the second with 26 subjects. Mr. X is a subject in the first data set and is associated with a value of 66. In the first set, 3 values are ranked behind 66 and 11 values are ranked ahead of it (with Mr) X being the other data value). In the second set, 9 values are ranked behind 66 and 16 values are ranked ahead of it. What is Mr. X's rank in a Wilcoxon rank sum test?