Business Statistics Homework #4, Spring 2014

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1 Business Statistics Homework #4, Spring 2014 This homework assignment is due at the beginning of class on May 2, Instructions: For all problems, use the 7 Steps in Hypothesis testing and round all z and t-values to 2 decimal places. Small samples are collected from normally distributed populations. Large samples are collected from populations with an unknown distribution. Problem SKF is the largest bearing manufacturer in the world and employs approximately 44,000 people in approximately 100 manufacturing sites that span 70 countries. For the SKF C301 ball bearing, the specification of its diameters is 0.50 centimeters. Ball bearings with diameters smaller or larger than 0.50 centimeters are undesirable. In April, a shipment from SKF of 200,000 C301 ball bearings was received by General Electric. A sample of 120 ball bearings was tested to see if the average diameter fulfilled the above specification. The sample average diameter was 0.51 centimeters with a sample standard deviation of 0.06 centimeters. Should General Electric keep this shipment or return the ball bearings to SKF? a) Interpret your results with 90% confidence. b) Interpret your results with 95% confidence.

2 Problem Textbooks prices are outrageous. Students spend an average of $1,200 a year on textbooks and course materials. Prices have been rising more than four times the rate of inflation for the past two decades! More students are choosing to save money in textbook through discounted options such as renting, purchasing used books, and book swaps on campus. Antelope Bookstore in UNK advertises the average rental cost of its textbook is $45. A sample of 50 students in UNK was asked how much they spend on renting a textbook for spring semester. The average rental cost of the sample was $44 with a standard deviation of $4. a) Using =.05, can you concluded that the average rental cost of a text book paid by the student is lower than the amount claimed by the book store? b) Using =.10, is the average rental cost of a text book paid by the student is higher than the amount claimed by the book store?

3 Problem A key player in the U.S. steel industry, Nucor Corp. produces a wide variety of steel products that service all major end markets. Their fasteners are used in nonresidential construction including: buildings, bridges, stadiums, towers, and power plants. A307 bolts produced by Nucor should pass the Proof Load Test and Wedge Tensile Test before they can be used in slip critical joints of steel structures. The Tensile strength of A307 bolts must be greater than 60 ksi(kilogram per square inch) to pass the Wedge Tensile Test. The extended length (beyond the threaded nut) of A307 needs to be shorter than 12.5 micrometers to pass the Proof Load Test. Before 2,000 boxes of A307 bolts will be delivered to Nucor s distributor in Nebraska, a sample of 27 bolts were tested for their Proof Load and Wedge Tensile. The average minimum tensile strength was 63 ksi with a standard deviation of 6 ksi. The average extended length was 12.6 micrometers with a standard deviation of 2.7 micrometers in the Proof Load. Should Nucor deliver these bolts to Nebraska? a) Did Nucor A307 bolts pass the Wedge Tensile test? (Let ) b) What is the Type I error in this situation? What are the consequences of making this error? c) What is the Type II error in this situation? What are the consequences of making this error? d) Did Nucor A307 bolts pass the Proof Load test? (Let ) e) What is the Type I error in this situation? What are the consequences of making this error? f) What is the Type II error in this situation? What are the consequences of making this error?

4 Problem By now, you should be familiar with the idea that men are from Mars and women are from Venus. It s a metaphor meant to symbolize the differences between men and women, because whether you like it or not, science has proven we are different animals. Of course, some men and women will defy stereotypes, but in the insurance industry, majority rules, and men find themselves paying more for car insurance. A sample of 34 men resulted in a six-month insurance policy averaging $765 with a standard deviation of $161 while a sample of 40 women resulted in a six-month insurance policy averaging $698 with a standard deviation of $89. Test if men s six-month insurance policies cost more than women s six-month insurance policies. (Let =.02) Problem Nearly 83 percent of parents plan to include candy and chocolate in their Easter baskets this year, according to a nationwide survey by the National Confectioners Association (NCA). While other popular items for the Easter basket include non-edibles, such as crayons, stuffed animals and books (73 percent). A survey has been conducted in Kearney last week to test the claim that more than 80% of parents plan to include candy in their Easter basket, while 70% of parents plan to include books or animals in the basket. a) Out of the 50 Parents surveyed, 45 plan to put candy in Easter basket. Using, does the data support the claim that more than 80% of parents plan to include candy in their Easter basket? b) Likewise, in a sample of 83 parents, 56 plan to include books or animals in their Easter basket. With 90% confidence, does the data support the claim that more than 70% of parents plan to include books or animals in their basket?

5 Problem 6 In a poll conducted in January 2014, 18 percent of Internet-using adults claimed to have had important personal data stolen, such as their bank account information or Social Security number. In a similar poll from July 2013, only 11 percent of adults claimed to have been victims of data theft. A survey in California was taken to see if there is any difference from the national pool. Out of 113 Californians surveyed, 15 claimed that have had important personal data stolen. a) With 90% confidence, can you conclude that the proportion of Californians who claimed to have had important personal data stolen is less than the National proportion? b) ICANN, which is an organization ensuring the internet network's stable and secure operation, believes that the percent of Californians who have had important personal data stolen is larger than the national proportion in July At a.25 level of significance, does the survey support ICANN s belief? Problem 7 Additionally, we assume that the percentage of Californians who claims that that have had important personal data stolen on internet is 18%, same as the national level. You decided to break it down to the city level believing that Los Angeles would have a higher percentage of residents who had have important personal data stolen than San Francisco. A sample from each city was taken to see if your claim held true. Use the table below to determine if a higher percent of residents in Los Angeles claim that they had have important personal data stolen than San Francisco. Los Angeles San Francisco Number of adults sampled Number of adults have had important personal data stolen a) Interpret your results with 80% confidence. b) Interpret your results with 90% confidence.

6 Problem 8 U.S. Airlines vary in numerous ways. Researchers want to determine the factors which cause each airline to have different fleet sizes. In the Excel Spreadsheet Airlines, several U.S. Airlines are listed with the year they were founded and the number of destinations where they fly. Researchers believe that these two characteristics are what help determine the number of planes (fleet size) each airline owns. a) Using Excel, create a Scatter Graph for the fleet sizes by the year founded and a Scatter Graph for fleet sizes by the number of destinations. b) Use regression analysis to develop an estimated regression equation that could be used to estimate the airline's fleet size given the year in which it was founded. Write the regression equation. Use the 7 steps of hypothesis testing to see if the year in which the airline was founded is significant. c) Use regression analysis to develop an estimated regression equation that could be used to estimate the airline's fleet size given the number of airline destinations. Write the regression equation. Use the 7 steps of hypothesis testing to see if the number of airline destinations is significant.