Evaluate total sum of squares

Reference no: EM138003

1. 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 16 volunteer subjects, 8 men and 8 women per group, were divided on the basis of age. 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 under 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." 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.

1484_Normal distribution.png

The pooled standard deviation is

A. 1.997.
B. 2.031.
C. 4.126.

2. A researcher is studying treatments for agorophobia with panic disorder. The treatments are to be the drug Imipramine at the doses 1.5 mg per kg of body weight and 2.5 mg per kg of body weight. There will also be a control group given a placebo. Thirty patients were randomly divided into three groups of 10 each. One group was assigned to the control, and the other two groups were assigned to each of the two treatments. After 24 weeks of treatment, each of the subject's symptoms were evaluated through a battery of psychological tests, where high scores indicate a lessening of symptoms. Assume the data for the three groups are independent and the data are approximately Normal. The means and standard deviations of the test scores for the three groups are given below.

The total sum of squares is

A. 3727.8.
B. 8393.5.
C. 12121.3.

Reference no: EM138003

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Normal distribution : 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.

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