Hypothesis Testing with Normal Distribution: Bicycle Crank Arms and IQ Scores, Quizzes of Probability and Statistics

Download Hypothesis Testing with Normal Distribution: Bicycle Crank Arms and IQ Scores and more Quizzes Probability and Statistics in PDF only on Docsity! Quiz # 5 May 12, 2008 Name: Directions: Make sure to read each problem carefully. Make sure to show all of your work to receive full credit. The bicycle parts company Onamihs produces bicycle crank arms (the part that attaches the pedal to the bicycle’s frame) that are listed at 170 mm in length. They hire a new quality control expert who thinks that their crank arms are actually a bit longer than that. He randomly picks 100 crank arms and finds that their average length is x̄ =170.08 mm. Suppose that the length of these crank arms are Normally distributed with standard deviation σ =0.5 mm. Problem 1. The quality control expert wishes to proceed with this hypothesis test. What should his null and alternative hypotheses be? a) H0 : µ =170 mm, Ha : µ 6=170 mm b) H0 : µ >170 mm, Ha : µ =170 mm c) H0 : x̄ =170 mm, Ha : x̄ 6=170 mm d) H0 : x̄ =170 mm, Ha : x̄ >170 mm e) H0 : µ =170 mm, Ha : µ >170 mm f) none of the above Problem 2. Next, he wants to know what his z test statistic is. (Make sure to show your work) a) z = −1.6 b) z = 0.16 c) z = 1.6 d) z = 16 e) z = 0.08 f) none of the above Problem 3. Second guessing himself, he ran the test again and this time he got a z test statistic of z = 1.23. What would his P-value be in this case? a) P = 0.2186 b) P = 0.5478 c) P = 0.1093 d) P = 0.8907 e) P = 1.8814 f) none of the above