Download Supplemental Problems for Hypothesis Testing in Math 218 - Prof. Lin and more Exams Mathematics in PDF only on Docsity! Math 218 (Fall 2008) Supplemental Problems for Hypothesis Testing TA: Wei Lin I. Testing for a Mean 1. (Spring 2005, 8) The owner of a downtown parking lot suspects that the average time cars use the parking lot is actually greater than the one reported by the person she hired to run the lot. The receipts as provided by the employee indicate that, on average, each car is parked for 3.5 hours. To determine whether the time parked is actually greater than the 3.5 hours reported by the employee, the owner observed 141 cars and noticed that the time spent on the lot by those cars was on average 3.73 hours with a sample standard deviation of 1 hour. Assume that the amount of time cars are parked is normally distributed. (a) Formulate the null and the alternative hypotheses. (b) Determine the test statistic. Evaluate it numerically. (c) Estimate the p-value. Circle the correct range for the p-value. < .5% [.5%, 1%) [1%, 2.5%) [2.5%, 5%) ≥ 5% (d) Can the owner conclude at the 1% significance level that the time parked is actually greater than 3.5 hours? (e) Suppose that the standard deviation of the time cars are parked in the parking lot is known and is σ = 1 hour. If the real mean time cars are parked in the parking lot is 3.6 hours, determine the probability of a type II error at a 1% significance level. 2. (Fall 2003, 9) The Healthy Food company claims that its cereal boxes contain, on average, 453 grams of cereal. We suspect that the cereal boxes contain, on average, less than claimed. You decide to test the claim by inspecting 6 randomly selected boxes, and get the following weights: 454, 447, 452, 446, 450, 445. Assume that the amount of cereal in a box follows a normal distribution. (a) Formulate the null and the alternative hypotheses. (b) Which statistic should be used to test these hypotheses? Evaluate it numerically. (c) Formulate the rejection rule at 5% significance level. Using your computation in (b), decide whether the null hypothesis should be rejected. (d) At which of the following significance level(s) should the null hypothesis be rejected? Circle all that apply. 0.005 0.01 0.025 0.05 0.1 3. (Fall 2000, 10) The height of American adult males is normally distributed with a mean of 69.1 inches. A new drug to combat math anxiety is discovered but it is suspected that when used by children it may affect the child’s growth. The FDA commissions a long term study to ascertain if there is any evidence for this assertion. (a) Formulate the null and alternative hypotheses and choose an appropriate test statistic. (b) In the FDA study 20 children that took the drug regularly between the ages of 8 and 10 years are monitored until they are adults. It is found that their height as adults has an average of 70.0 inches and a sample standard deviation of 2.1 inches. Calculate the value of the test statistic. Then estimate the p-value and justify your answer. p-value is (circle one): (i) less than 0.005 (ii) 0.005 to 0.01 (iii) 0.01 to 0.025 (iv) 0.025 to 0.05 (v) 0.05 to 0.10 (vi) 0.10 to 0.20 (vii) more than 0.20 1
