Posted by **Haley** on Tuesday, June 5, 2007 at 7:25pm.

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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