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STAT 200 Week 6 Homework
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18. You choose an alpha level of .01 and then analyze your data.

a. What is the probability that you will make a Type I error given that the null hypothesis is true?

The probability of type I error is actually alpha given that the null hypothesis is true so it is 0.01.

b. What is the probability that you will make a Type I error given that the null hypothesis is false?

When null hypothesis is false, it is impossible to make a type I error. It means probability that you will make a type I error given that the null hypothesis is false is zero.

7. Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects get- ting better each trial? Test the linear effect of trial for the data.

 a b c 4 6 7 3 7 8 2 8 5 1 4 7 4 6 9 2 4 2

a. Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.

 L1 -1*4+0*6+1*7=3 L2 -1*3+0*7+1*8=5 L3 -1*2+0*8+1*5=3 L4 -1*1+0*4+1*7=6 L5 -1*4+0*6+1*9=5 L6 -1*2+0*4+1*2=0

b. Compute a one-sample t-test on this column (with the L values for each subject) you created.

M=Sample Mean = (3+5+3+6+5+0)/6 = 3.667

Standard error of mean = Sm = 2.160/sqrt(6) = 0.8819

t=(M-mu)/Sm = 3.667/0.8819 = 4.158

Using calculator, we find out the probability of two tailed test to be 0.0088

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