Reading highway signs is not always easy, especially if your vision is imperfect
ID: 3158533 • Letter: R
Question
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 and the extent to which age affects the distance at which a standard highway sign can be recognized. Three groups of sixteen volunteer subjects, eight men and eight women per group, were divided on the basis of age. Ages in Group 1 ranged from nineteen to thirty-five, in Group 2 from thirty-seven to fifty-nine, and in Group 3 from sixty-one to seventy-six. 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 under daylight conditions. Sign size increased in small increments until the subjects were able to describe the sign satisfactorily. The smallest size at which the sign could be clearly described was called the "threshold." Mean threshold values and standard deviations for the three groups are given below. Normal probability plots showed the three populations were well approximated by the Normal distribution.
Group Means Std. Devs.
1 10.41 2.43
2 9.47 2.04
3 7.97 1.52
Which of the following is true?
A. The results from the one-way ANOVA may not be correct because all the standard deviations are not greater than 2.
B.The results from the one-way ANOVA will be approximately correct because all the means are larger than 2.
C. The results from the one-way ANOVA will be approximately correct because the largest standard deviation is less than twice the smallest standard deviation.
Explanation / Answer
We are given three groups, so we can use one-way ANOVA to analyze mean. One-way ANOVA assumes that all three groups have same variance. Wesay variances are same when the largest standard deviation is less than twice the smallest standard deviation. Therefore, the correct option is:
C. The results from the one-way ANOVA will be approximately correct because the largest standard deviation is less than twice the smallest standard deviation.
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