Assign 8 1 PLEASE SHOW ALL WORK The Survey of Study Habits a

Assign. 8 #1 PLEASE SHOW ALL WORK

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students\' study habits and attitudes toward school. Scores range from 0 to 200. The mean score for college students is about 112, and the standard deviation is about 29. A teacher suspects that the mean mu for older students is higher than 112. She gives the SSHA to an SRS of 28 students who are at least 30 years old. Suppose we know that scores in the population of older students are Normally distributed with standard deviation sigma = 29. We seek evidence against the claim that mu = 112. What is the sampling distribution of the mean score x of a sample of 28 students if the claim is true? Sketch the density curve of this distribution. (Sketch a Normal curve, then mark the axis using what you know about locating the mean and standard deviation on a Normal curve. Do this on paper. Your instructor may ask you to turn in this work.) Suppose that the sample data give x = 115.6. Mark this point on the axis of your sketch. In fact, the result was x = 122.8. Mark this point on your sketch. (Do this on paper. Your instructor may ask you to turn in this work.) Using your sketch, explain in simple language why one result is good evidence that the mean score of all older students is greater than 112 and why the other outcome is not. If mu = 112, observing a value of 122.8 would not be too surprising, but 115.6 is less likely, and therefore provides some evidence that mu 112.

Solution

a)
If the claim is true, then we have the same mean, and then the standard deviation of the mean will be the original divided by sqrt(n).

Thus,

Mean = 112
Standard deviation = sigma/sqrt(n) = 29/sqrt(28) = 5.480484859 [answer]

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b)

If u = 112,

*115.6 would not be surprising, as it is still near 112 (it\'s not even 1 standard deviation away),

*122.8 is less likely, as it is farther from the mean.

Thus, 122.8 provides some evidence that u > 112.

There, the answer is [OPTION D, ANSWER].