41. A new material is being tested for use in the manufacture of electrical conduit, to determine whether it will reduce the variance in crushing strength over the old material. Crushing strengths are measured for a sample of size 16 of the old material and a sample of size 20 of the new material. If it is shown that the crushing strength with the new material has smaller variance, the new material will be used. 5. Suppose you have purchased a filling machine for candy bags that is supposed to ll each bag with l on of candy. Assume that the weights of lled bags are approximately normally distributed. Arandom sampie of it] bags yields the foiloyn'ng data (in or]: 15.8T"l.021533153315691531 16.0415.3115.92 16.111] [in the basis of these data, can you conclude that the mean ll weight is actually less than 15 oz? a) State the appropriate null and alternate hypotheses. b} Compute the value of the test stastic. c) Find the Pyalue and state your conclusion. . Are answer keys to multiplechoice tests generated randomly, or are they constructed to make it less likely for the same answer to occur twice in a row? This question was addressed in the article "Seek 1iriihence: Answer Sequences and Their Consequences in Key-Balanced MultipleChoice Tests" (M. BarHillel and Y. Attali, The American Statistician, 22:2993IJ3}. They studied 1230' questions on It] real Scholastic Assessment Tests (SATs). Assume that all the questions had ve choices [in fact 150 of them had only four choices]. They found that for 192 of the questions, the correct choice (A, B, C, D, or E] was the same as the correct choice for the question immediately preceding. If the choices were generated at random, then the probability that a question would have the same correct choice as the one immediately preceding would be [1.211 Can you conclude that the choices for the SAT are not generated at random? a) State the appropriate null and alternate hypotheses. b} Compute the value of the test statistic. c) Find the Pyalue and state your conclusion. T. An automobile manufacturer wishes to compare the lifetimes of two brands of tire. She obtains samples of seven res of each brand. [in each of seven cars, she mounts one re of each brand on each front wheel. The cars are driven until only 20% of the original tread remains. The distances, in miles, for each re are presented in the following table. Can you conclude that there is a difference between the mean lifetimes of the two brands of re? Car Brand Brand 2 l 1 35,025 34,313 45,300 42,200 35,240 35,500 32,100 31,350 32,210 33,015 Ulla-WM