A manufacturer of automobile batteries claims that at least 80% of the batteries, that it produces will last 36 months. A consumers' advocate group wants to evaluate this longevity claim and selects a random sample of 28 batteries to test. The data below indicate the length of time (in months) that each of these batteries lasted (i.e., performed properly before failure). 42.3 39.6 25.0 56.2 37.2 47.4 57.5 39.3 39.2 47.0 47.4 39.7 57.3 51.8 31.6 45.1 40.8 42.4 38.9 42.9 34.1 49.0 41.5 60.1 34.6 50.4 30.7 44.1 We wold like to test, at a significance level of 0.05, if there is a significant evidence that less than 80% of the batteries will last at least 36 mont hs? a. State the null and alternative hypothesis (in mathematical terms and state what the symbols you use in the statements represents). b. What is the test statistics that you would use? c. What is the distribution of the test statistics? d. What is the decision rule? e. What is your conclusion, based on the sample above?