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MATH 107 HW #9 Due Tuesday, March 17 PART I 1. A bank has recently acquired a new branch and thus has customers in this new territory. They are interested in the default rate in their new territory. They wish to test the hypothesis that the default rate is different from their current customer base. They sample 200 files in area A, their current customers, and find that 20 have defaulted. In area B, the new customers, another sample of 200 files shows 12 have defaulted on their loans. At a 10 % level of significance, can we say that the default rates are the same or different? 2. Two types of valves are being tested to determine if there is a difference in pressure tolerances. Fifteen out of a random sample of 100 of Valve A cracked under 4,500 psi. Six out of a random sample of 100 of Valve B cracked under 4,500 psi. Test at a 5 % level of significance. 3. The mean emission of all engines of a new design needs to be below 20 ppm if the design is to meet new emission requirements. Ten engines are manufactured for testing purposes, and the emission level of each is determined. The emission data is: 15.6, 16.2, 22.5, 20.5, 16.4, 19.4, 16.6, 17.9, 12.7, 13.9 . Does the data supply sufficient evidence to conclude that this type of engine meets the new standard? Assume α = .01. 4. Do you have food cravings? According to the New York Times, one of the largest studies of food cravings involved a survey of 1000 McMaster University students. The survey revealed that 97 % of the women in the study acknowledged specific food cravings while only 67 % of the men did. Assume that 600 of the respondents were women and 400 were men. (a) Is there sufficient evidence to claim that the true proportion of women who acknowledge having food cravings exceeds the corresponding proportion of men? Test using α = .01. (b) Why is it dangerous to conclude from the study that women have a higher incidence of food cravings than men? 5. Many female undergraduates at four-year colleges switch from STEM majors into disci- plines that are not science-based, thereby contributing to the underrepresentation of women in STEM fields. When female undergrads switch majors, are their reasons different from those of their male counterparts? This question was investigated in Science Education. A sample of 335 junior/senior undergraduates- 172 females and 163 males- at two large research universities were identified as “switchers”, that is they left a declared STEM major for a non-STEM major. Each student listed one or more factors that contributed to the switching decision. (a) Of the 172 females in the sample, 74 listed lack or loss of interest in STEM (i.e., “turned off” by science) as a major factor, compared to 72 of the 163 males. Conduct a test (at α = .10) to determine whether the proportion of female switchers who give “lack of interest in STEM” as a major reason for switching differs from the corresponding proportion of males. (b) Thirty–three of the 172 females in the sample indicated that they were discouraged or lost confidence because of low grades in STEM during their early years, compared to 44 of 163 males. Construct a 90 % confidence interval for the difference between the proportions of female and male switchers who lost confidence due to low grades in STEM. Interpret the result. Note: Do a search for Confidence Intervals on YouTube. The Khan Academy has a great one. It’s directly linked to what we’ve been doing, as you’ll see, and I’m preparing you for the way things will be if school closes because of COVID.