A test will be" conducted to see how long a seven-ounce tube of toothpaste lasts. The researcher wants to establish that the mean time is greater than 30.5 days. From a random sample of size 75, an investigator obtains  = 32.3 and s = 6.2 days.
(a) Formulate the null and alternative hypotheses. (Define any symbols you use.)
(b) Determine the test statistic.
(c) Give the form of the rejection region.
(d) What is the conclusion to your test? Take α = .10.
(e) Calculate a P-value.
(f) Based on part (d), what error could you have possibly made?