Question

A chemist made eight independent measurements of the melting point of tungsten. She obtained a sample mean of 3410.14 degrees Celsius and a sample standard deviation of 1.018 degrees.

B. The chemist is interested in variation of her measurements. Use the same of eight independent measurements to do the following.

(i) Conduct a hypothesis test to determine whether or not the population standard deviation differs from 0.75 degrees Celsius. Use α = 0.01 to make your conclusions. Be sure to state your hypotheses, test statistic, and conclusions.

Hint: To make your conclusions, compute χ 2 lower and χ 2 upper. If the test statistic χ 2 satisfies χ 2 lower ≤ χ 2 ≤ χ 2 upper, do not reject H0. Otherwise, reject H0 in favor of H1.

(ii) Construct a 99% two-sided confidence interval for the population standard deviation. Compare the CI with the results of the hypothesis test in (ii). Are the conclusions consistent?

Next modify to get a CI for the population standard deviation.

Answer 1

i)

The test statistic is

    

   

At alpha = 0.01, the critical values are

Since the test statistic value lies between the critical values(0.9893 < 12.896 < 20.2777), so we should not reject the null hypothesis.

Do not reject H₀.

ii) The 99% confidence interval for population standard deviation is

Since the interval contains the hypothesized value 0.75, so we should not reject the null hypothesis.