Lab 2 Let's say a mechanical engineer is designing a car lift that uses cables to bear the weight of the car. They buy cable from a supplier who claims it has an ultimate tensile strength of 1800 lbs with standard deviation of 100 lbs. The engineer thinks the supplier might be overestimating their cable strength, and wants to check if the ultimate tensile strength is really as high as the supplier claims, or if it actually lower. They test samples of the cable to get the following data for the strength of the cable: UTS cable = [1767, 1681, 1791, 1748, 1734,... 1703, 1781, 1590, 1735, 1720, ... 1683, 1840, 1701, 1829, 1872] UTS cable = 115 1767 1681 1791 1748 1 1734 1703. 1. (2pts) Give the null and alternative hypotheses that the engineer wants to test. Is the test one- or two- tailed? How do you know? 2. (2pts) Write a function to calculates a z-score and t-score for a set of data using inputs: the list of data as an (nx1) vector, the null hypothesis mean, and the population standard deviation. Use your function to determine the z-score and t-score of the data. 3. (2pts) For this data set, should you use a t-test or z-test? Why? 4. (2pts) Using the appropriate calculated z- or t-score, calculate the corresponding p-score with the appropriate formula from class. Based on this and using a value of 0.05 for a, do we have sufficient data to show that the supplier's claims were high, or are they accurate? 5. (2pts) Check your results using the ttest command. Run the t-test using a value of 0.01 for a as well. Do you get the same results? 6. (2pts) If one value of a would cause us to reject the null hypothesis while another value would cause us to reject the alternative hypothesis, what does this mean for our results? How can this discrepancy be addressed?