20 47 Statistics: Assignment 26.20 Name: The manager of Acme Widget Company wants to increase worker productivity. She records the number of widgets produced by each of 10 workers between 10:30 and 11:30 on a Tuesday. The next week she replaces the coffee served in the break room with a new brand that contains extra caffeine. She again records the number of widgets produced by the same workers between 10:30 and11:30 on Tuesday. Employee # 3. 4. 9. 8. 6. Widgets produced during first week 28 11 25 34 31 21 16 45 Widgets produced after break 12 23 22 38 24 room coffee replaced The manager wants to see if, and by how much, productivity will increase when the break room serves coffee with extra caffeine. a) EXPLAIN WHY, you are choosing the type of test you feel is the most appropriate for this problem, a 2-Sample t-test or a paired differences test. b) Construct an appropriate 90% confidence interval, c) What would be the real world consequences if this test results in a Type I error? d) Perform a hypothesis test at the 5% significance level which will determine whether there is evidence that productivity increases if the break room coffee is replaced with a brand containing extra caffeine. Statistics: Assignment 27.10 Name: Suppose we asked the (self described) head-of-household in 180 Alaska households two questions: "Does your family own a gun?" And "Do you believe criminals who commit first degree murder should face The Death Penalty?" In our sample, 100 households owned a gun and 70 of them favored the death penalty. Of the remaining 80 households who did not own a gun, 44 favored the death penalty. The data are summarized in the table below. Owns a Gun Yes No. 44 Total Favors the Death Yes 114 Penalty for Murderers No 30 99 Total 08 081 a) Consider these samples from two populations; those who own guns, and those who don't. Consider it a 'success' if they favor the death penalty. Perform a hypothesis test where the alternate hypothesis is that the proportion of gun owners who favor the death penalty is different from the proportion of non-owners who favor the death penalty. Hi: %3D = 'd = °d =D Z p-value %3D Reject Ho or Fail to reject Ho Conclusion (in a sentence or two): b) Now, let's split up the groups the other way. Consider these samples from two populations; those who favor the death penalty, and those who don't. Consider it a 'success' if they own a gun. Perform a hypothesis test where the alternate hypothesis is that the proportion of those who favor the death penalty who own a gun is different from the proportion of those who don't favor the death penalty that own a gun. Hi: = 'd = "d %3D p-value = Reject Ho or Fail to reject Ho Conclusion (in a sentence or two): 17 To Do Notifications xoqui