UFO Sighters\' Personalities In a 1993 study, researchers took a sample of peopl
ID: 3063170 • Letter: U
Question
UFO Sighters' Personalities In a 1993 study, researchers took a sample of people who claimed to have had an intense experience with an unidentified flying object (UFO) and a sample of people who did not claim to have had such an experience (Spanos et al., 1993). They then compared the two groups on a wide variety of variables, including IQ. The group of 25 people who claimed to have had an intense experience with a UFO had a mean IQ of 101.6, and the standard deviation of these IQs was 8.9. A control group of 53 community members who had not reported UFO experiences had a mean IQ of 100.6 with a standard deviation of 12.3.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.4542
DF = 76.0
t = [ (x1 - x2) - d ] / SE
t = 0.41
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 76 degrees of freedom is more extreme than -0.41; that is, less than -0.41 or greater than 0.41.
Thus, the P-value = 0.683
Interpret results. Since the P-value (0.683) is greater than the significance level (0.05), we have to accept the null hypothesis.
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