1. Last year, the weekly price of a 4-litre container of milk averaged $3.89 with a standard deviation of $0.40. A consumer advocacy group wishes to test if the price of a 4-litre container of milk is higher compared to last year. It is assumed that the standard deviation in the weekly price of milk has stayed the same in 2010.
(a) State the most appropriate null and alternative hypothesis.
(b) To test the null hypothesis stated in (a), the consumer advocacy group randomly selected n = 35 weeks out of the year, observing the price of milk on every Monday of each chosen week. The average price of milk was found to be X = $4.10. Using this information, find the value of the test statistic produced by the sample.
(c) Testing at α = 0.05, does the result in (b) support the null hypothesis in (a)? Ensure your answer is statistically justified.
(d) Find the P -value of the result in (b).
(e) In the context of the problem, interpret the meaning of the P -value found in (d).
(Note: An interpretation is NOT a decision rule!)