# Calculate the sample medians

Questions 47 through 50 are based on the following scenario.

Three neighbors are having a dispute over whose dog runs the fastest. They decide to do a little experiment. Each dog will run a short distance three times and their times will be recorded. Neighbor Warner knows a little about statistics and decides to use a Kruskal Wallis test. The times (in seconds) for the three dogs are listed below.

Jake

11.0

12.9

12.1

Rover

13.5

10.8

14.1

Molly

9.9

13.6

12.8

47.Calculate the sample medians for the three dogs. Based on the sample medians, which dog do you think is the fastest dog?

48.When we perform an ANOVA test, we have to assume that the standard deviations of the normal distributions that model the population distributions are equal. What is the equivalent assumption for the Kruskal Wallis test?

49.SPSS output is provided below. What is the value of the test statistic?

50.State your decision at the 10% significance level. What would you tell the 3 neighbors?

Questions 51 through 57 describe various scenarios. State the best nonparametric or parametric test for each situation. (Important: Some of these studies are best analyzed with the parametric tests learned in other chapters)

51.An undergraduate student wants to go into a field with high job security, and is told that a given field has a median longevity rate (before switching careers) of 22 years. She samples 50 people who have retired, but were in this field at one point, and asks them how many years they worked in the field. Is the median of 22 years accurate?

52.A clinician wonders whether her morning or afternoon appointments were more likely to be on time. She looks over her records from the past year, and takes a random sample of 150 people who came in the morning and 150 who came in the afternoon and notes how many minutes late each one was, marking a zero for on-time clients. These data are expected to be skewed to the right due to a few very late clients.

53.A researcher wondered whether family size is affected by religion. He obtained the number of children from four Roman Catholic families, four Baptist families, three Jewish families, and three Muslim families. Due to the occasional very large families, the data are expected to be skewed to the right.

54.A preschool teacher wonders whether a book program will reduce the amount of television that her students watch. Of the nine children in her preschool class, she randomly assigns five to the program. The other four do not receive the program. The hours of TV watching are expected to be skewed to the right because of the few students who watch a ton of TV.

55.A superintendent of schools wonders whether a book program will reduce the amount of television that students watch. She has her assistants assess the TV watching of 200 high school students. The book program is then implemented with all 200 students. Following the program, the assistants again assess the TV watching of the students. The hours of TV watching are expected to be skewed to the right because of the few students who watch a ton of TV.

56.A researcher wondered whether family size is affected by religion. He obtained the number of children from 400 Roman Catholic families, 400 Baptist families, 380 Jewish families, and 380 Muslim families. Due to the occasional very large families, the data are expected to be skewed to the right.

57.A preschool teacher wonders whether a book program will reduce the amount of television that her students watch. She assesses the TV watching of the nine children in her preschool class. She then conducts the program with all nine students. Following the program, she again assesses the TV watching of her students. The hours of TV watching are expected to be skewed to the right because of the few students who watch a ton of TV.