STAT260Final_longVerB

STAT 260 A01 & A02 - Final Exam Long Answer Portion (Version B) Wednesday April 21st, 2021 • For this part of the test, please handwrite your solutions on paper or electronically, scan, and upload your solutions to the submission link on Crowdmark. • This portion of the test contains 3 questions (with multiple parts). • For these questions, write out your solutions carefully and completely. Marks will be deducted for incomplete or poorly presented solutions. You must use correct notation and show all steps in your work. • Solutions requiring the use of a stat table should be completed using our Stat 260 Distribution Tables. • Remember to also complete and submit the Short Answer Portion of the test on Brightspace. • Your solutions for both parts of the final exam are due at 4pm (PDT) (unless you have a pre- approved time accommodation). You do not need to submit this cover page of instructions. Remember that as this is a test you are required to solve questions on your own wit- hout outside help. This includes the use of internet resources outside of the material found on your course Brightspace page and the help of other people. Students must not communicate with each other during the test.

April 21st, 2021 STAT 260 [A01 & A02] Final Exam - Version B Page 1 of 6 The following questions require full answers. You must use correct notation and show all steps in your work. 1. In a study we are comparing the lifespans of batteries made by two manufacturers. We have randomly selected 12 batteries from Company A and 10 batteries from Company B. The data on battery lifespan is summarized in the table below. (Note: SD = standard deviation.) Company Sample Size Sample Average Sample SD Company A n 1 = 12 x 1 = 60 . 5 s 1 =6.5 Company B n 2 = 10 x 2 = 70 . 3 s 2 =8.5 Is there evidence that the mean lifespan (in hours) for the batteries made by Company A is less than those made by Company B? If needed, you may assume that the population(s) is(are) normally distributed. (a) [2 marks] Define the parameter(s) of interest using the correct notation. Then, state the null and alternative hypotheses for this study. (b) [2 marks] Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows.

April 21st, 2021 STAT 260 [A01 & A02] Final Exam - Version B Page 3 of 6 2. A particular brand of car tire has a suggested air pressure of 30 pounds per square inch (psi). As part of a typical annual service a mechanic will check the tire pressure when a car is brought in. Let X denote the tire pressure (in psi) found on the left front tire and let Y denote the tire pressure (in psi) of the right front tire. The joint probability distribution of X and Y is given by: x p ( x, y ) 25 30 40 25 0 . 06 0 . 08 0 . 11 y 30 0 . 05 0 . 10 0 . 04 40 0 . 13 0 . 24 0 . 19 (a) [2 marks] The mechanic is asked to service a random car. What is the probability that at least one of the front tires is above the suggested air pressure? That is, find P ( X > 30 ∪ Y > 30). (b) [2 marks] Calculate E ( XY ).

April 21st, 2021 STAT 260 [A01 & A02] Final Exam - Version B Page 4 of 6 (c) [3 marks] Calculate the correlation coefficient of X and Y , Corr ( X, Y ). (Note: as part of your calculation you will need to find the covariance of X and Y , Cov ( X, Y ).) (d) [1 mark] Based on your answer to part (d), is there a strong linear relationship between X and Y ? Explain. (e) [1 mark] Are X and Y independent? (Hint: this should involve a calculation. You may refer to calculations completed in previous parts of this question.)

April 21st, 2021 STAT 260 [A01 & A02] Final Exam - Version B Page 6 of 6 (c) [1 mark] Compute the p -value or provide a range of appropriate values for the p -value within the accuracy of the tables . (d) [1 mark] If we were testing our hypotheses at the level α = 0 . 05, what would our conclusion about the proportion of leaking faucets with this new design be? In order to receive a mark, you must state how you made your decision. - END OF TEST - - SUBMIT YOUR SOLUTIONS TO THIS PORTION AND THE SHORT ANSWER PORTION - - Have a good summer! -