Option 1
Researchers were interested in whether the use of biases in reasoning depended upon a person\’s intelligence. The researchers divided their sample of college freshman into two groups: those of higher intelligence and those of lower intelligence. They then gave both groups of students a test of reasoning.
a. If the researchers reject the null hypothesis, what is their conclusion?
b. If the researchers do not reject the null hypothesis, what is their conclusion?
c. If the researchers make a type I error, what does this mean?
d. If the researchers make a type II error, what does this mean?
Option #2:Statistically significant difference refers to a difference that is unlikely to have occurred by chance, given the size of the difference, the sample size, and the consistency of the scores (standard deviation). Explain why researchers who find that a difference is not statistically significant cannot assume that no difference exists. (This was discussed in the notes for unit 7.) For example, researchers were trying to determine if drug XXX, administered during infancy, resulted in cognitive impairments. They identified 10 children who had taken drug XXX as infants and tested the IQ score for these children. The average IQ score for these children was 90.8. They compared that to the national average, which is 100, with a standard deviation of 15. Based on these numbers, they calculated a z statistic of – 1.94. (See calculation below.) This calculated value of z does not exceed the critical value of z at the .05 level of significance (1.96), so the researchers cannot reject the null hypothesis; the difference is not statistically significant. Does this prove that drug XXX is safe? That is, since the difference was not found to be statistically significant, can we conclude that children that were treated with drug XXX were no different in measured intelligence than those who were not exposed to drug XXX? Explain why or why not.
M = 15/10 = 4.74
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