Finding the unbiased estimator of variance

Question

The information that I've been given:

After a chemical spillage at sea, a scientist measures the amount, x units, of the chemical in the water at 15 randomly chosen sites. The results are summarized in the form ∑x=18 and ∑x^2=28.94. Before the spillage occurred the mean level of the chemical in the water was 1.1. Test at the 5 % significance level the hypothesis that there has been an increase in the amount of the chemical in the water.

To solve this question, I'll need to the value of the unbiased estimator of the variance which is: 0.524.

I'm unable to apply the appropriate formula and get it.

What I know: Unbiased estimator of variance: (n/n-1) * (sample variance)

score 1 · Accepted Answer · answered Apr 20 '20 at 04:41

1

Hint: The (raw, biased) sample variance of $n$ measurements $x_i$ can be obtained by the formula $$\sigma^2=\left(\frac1n\sum x^2\right)-\left(\frac1n\sum x\right)^2$$

answered Apr 20 '20 at 04:41

Parcly Taxel

103,344

Thank you, got it! – Math Comorbidity Apr 20 '20 at 04:44
Yep that's what I plan to do. Though my 5 minute limit to accept answers will finish in the next 50 seconds. – Math Comorbidity Apr 20 '20 at 04:49

Finding the unbiased estimator of variance

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