Assignment:
Technology Project STATDISK, Minitab, Excel, the TI-83/84 Plus calculator, and many other statistical software packages are all capable of generating normally distributed data drawn from a population with a specified mean and standard deviation. IQ scores from the Wechsler Adult Intelligence Scale (WAIS) are normally distributed with a mean of 100 and a standard deviation of 15. Generate two sets of sample data that represent simulated IQ scores, as shown below.
IQ Scores of Treatment Group: Generate 10 sample values from a normally distributed population with mean 100 and standard deviation 15.
IQ Scores of Placebo Group: Generate 12 sample values from a normally distributed population with mean 100 and standard deviation 15.
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STATDISK:
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Select Data, then select Normal Generator.
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Minitab:
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Select Calc, Random Data, Normal.
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Excel:
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If using Excel 2007, select Data; if using Excel 2003, select Tools.
Select Data Analysis, Random Number Generator, and be sure
to select Normal for the distribution.
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Plus: TI-83/84
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Press  , select PRB, then select randNorm( and enter the
mean, the standard deviation, and the number of scores (such as
100, 15, 10).
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You can see from the way the data are generated that both data sets really come from the same population, so there should be no difference between the two sample means.
a. After generating the two data sets, use a 0.10 significance level to test the claim that the two samples come from populations with the same mean.
b. If this experiment is repeated many times, what is the expected percentage of trials leading to the conclusion that the two population means are different? How does this relate to a type I error?
c. If your generated data should lead to the conclusion that the two population means are different, would this conclusion be correct or incorrect in reality? How do you know?
d. If part (a) is repeated 20 times, what is the probability that none of the hypothesis tests leads to rejection of the null hypothesis?
e. Repeat part (a) 20 times. How often was the null hypothesis of equal means rejected? Is this the result you expected?