Question

The manufacturer of an antibiotic must ensure that each 5 mL dose contains 250 mg of the
active ingredient. It is also essential that the variance of the amounts of active ingredient per
dose be less than 0.1. For testing purposes, a random sample of 96 doses is taken, and the
variance of the amounts of active ingredient per dose in the sample is found to be 0.09. Does
this evidence support the claim that the variance is within the necessary bounds at the 0.01
level of significance?
(a) (3 points) State the null and alternative hypotheses H0 and Ha.
(b) (2 points) Identify which distribution to use for the test statistic. If applicable, calculate
the number df of degrees of freedom; if not applicable, then say so.
(c) (2 points) Compute the value of the test statistic z, t, or χ
2
.
(d) (2 points) Compute the p-value associated to the test statistic.
(e) (1 point) Choose whether or not to reject the null hypothesis H0.

Answer 1