QUESTION 3 (25 Marks) A manufacturer claims that the mean capacity of a certain type of battery the company produced is at least 140 ampere-hour. An independent consumer protection agency wishes to test the credibility of the manufacturer's claim and measure the capacity of a random sample of 20 batteries from a recently produced batch. The results, in ampere-hour, are average = 138.48 and standard deviation = 2.65. (a) (b) (e) (d) (e) (f) (9) Construct the appropriate null and alternate hypothesis for the manufacturer's claim. Explain your construction. State the decision rule and using the 0.05 level of signicance, conclude whether the manufacturer is overstating its claim. What must we assume i_r3_o_rder_tg perform the test in Question 3(b)? Is there evidence that the manufacturer's claim is being overstated if the last two capacity values of the random sample were 146.7 and 144.1 instead of 136.7 and 134.1 with a new standard deviation of 3.16? Would the construction of hypothesis be different if the manufacturer's claim is that the mean capacity of battery produced is 140 ampere-hour? Explain your construction. What sample size should the agency use if he wishes to estimate the true mean to be within an error of :l:0.5 ampere-hour with 95% condence? (Use the new standard deviation) (154) Compare and contrast the 3mm} t and standard normal 2 distributions. (Discuss this in relation to sample size