Example on chi-square approximation

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Reference no: EM138154

1. Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and soil treatment. An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides.
In a field containing 10 seedlings, six were randomly selected throughout the field and assigned to receive Herbicide A. The remaining seedlings were to receive Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide, and at the end of the study period the height (in cm) was recorded for each seedling. The following results were obtained:

If W, the Wilcoxon rank sum test statistic, is the sum of the ranks assigned to group Herbicide A, then W is equal to

A. 19.0.
B. 36.0.
C. 36.5.

2. Reading highway signs is not always easy, especially if your vision is imperfect. Vision in general tends to deteriorate with age. Two researchers conducted a study to determine if the distance at which a standard highway sign could be recognized changed with age. They investigated how much age affects the distance at which a standard sign is recognized. Three groups of 5 volunteer subjects were selected. Ages in group 1 ranged from 19-35, in group 2 from 37-59, and in group 3 from 61-76. All subjects had at least a high-school education and were active, licensed drivers in good health. Participants all met minimum vision requirements. Signs were shown to the subjects on a video monitor set up to imitate the way a person would see the signs while driving a car in daylight hours. Sign size increased in small increments until the subject was able to describe the sign satisfactorily. The smallest size at which the sign could be clearly described was called the "threshold." To see if the threshold sizes were systematically higher for some age groups than others, the data were ranked and the value of the Kruskal-Wallis statistic H = 7.1 was obtained. Using the chi-square approximation, the P-value for the test is

A. between 0.025 and 0.050.
B. between 0.050 and 0.100.
C. greater than 0.100.

Reference no: EM138154

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