I have a question on a quiz and I don't even know where to begin on figuring out the question... please help:
Measurements on the percentave of enrichment of 12 fuel rods used in a nuclear reactor were reported as follows:
3.11
2.88
3.08
3.01
2.84
2.86
3.04
3.09
3.08
2.89
3.12
2.98
Is there an indication that the rods do not meet a target of 2.95%? Assume alpha=0.05.
Also is there sufficient evidence to suggest that the variance is greater than 0.085? Assume alpha=.01.
First, calculate the mean (M), variance (V), and standard deviation (SD) of the observed sample.
Next, test whether the observed mean is significantly different from 2.95. Since this is a small sample (n=12), you will need to use a Students t distribution table (Your stats book probably has such a table). Your question implies a 2-tailed test with alpha=.05, so find the t-value which accounts for 97.5% of sample with (n-1) degrees of freedom. In my table, i get 2.201. Is your observed mean M within 2.201*SD of the target value of 2.95?
2) I get a variance (V) of 0.011, which of course, is less than .085. So no, there is not sufficient evidence to suggest the actual variance is greater than .085. That said, such a test would use a Chi-squared distribution table. I believe the chi-squared statistic is ((n-1)*V/.085)
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