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John oversees a bottle-filling machine in a company. The amount of fluid dispensed into each bottle is approximately normally distributed with an unknown population standard deviation. On a particular day, a random sample of 400 bottles yielded a mean of 357.2 ml and a standard deviation of 16.2 ml. John then concluded that the population standard deviation of the fluid dispense amount by the machine is greater than 15 ml. The lead engineer wants to use a 0.05 significance level to test John's claim.
(a) Identify the null hypothesis and alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support John's claim that the population standard deviation of the fluid dispense amount by the machine is greater than 15 ml? Explain.
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