# Statistics Question

I'm revising for my exams and I want to check if I did this exercise correctly:

10 measurements were done using a certain tool. The average and standard deviations of measurements using a this tool are 0.4495 and 0.014 respectively. Test, using a 5% significance level, wether or not the average measurement value deviates from the true value 0.45 and interpret the result.

What I have is:
My null-hypothesis is "the measurement doesn't deviate"
Alternative hypotheses: "The measurement deviates"

My test statistic, assuming null hypothesis, is $$T = \frac{0.4495-0.45}{0.014/\sqrt{10}} \approx -0.113$$ Now, $$|T| = 0.113 < t_{9, 0.025} = 2.262$$

This is not enough evidence to refute the null hypothesis, so it ends here?
Also, I apologise should my English be sub-par, I'm not natively English so feel free to correct me.

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## 1 Answer

The hypotheses for a two-tailed test are:

The null-hypothesis is "the (population) average measurement value equals 0.45".

Alternative hypothesis "the (population) average measurement value does not equal 0.45"

The T-statistic equals T=-0.113 and the associated p-value equals p=0.910 > 0.05. You therefore cannot reject the hypothesis that the true average is equal to 0.45 at the 5% significance level. Note that your sample is very small (n=10) so it will be difficult to find significant results.

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