Reading highway signs is not always easy, especially if your vision is imperfect

Question

Reading highway signs is not always easy, especially if your vision is imperfect. Vision tends to deteriorate with age. Two researchers conducted a study to determine if, (and, if so, the extent to which) age affects the distance at which a standard highway sign can be recognized. Three groups of 16 volunteers, eight men and eight women per group, were divided on the basis of age. Ages in Group 1 ranged from 19 to 35 years, in Group 2 from 37 to 59 years, and in Group 3 from 61 to 76 years. All volunteers 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 volunteers on a video monitor set up to imitate the way a person would see the signs while driving a car in daylight conditions. Sign size increased in small increments until the volunteers were 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

between 0.025 and 0.050.

greater than 0.100.

between 0.050 and 0.100.

Explanation / Answer

We have H = 7.1

Here X2 = Chi square

Now , P-value = P (X2 > H ) = P(X2 > 7.1 ) = 0.045185

Hence, Using the chi-square approximation, the P-value for the test is between 0.025 and 0.050.

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