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stats problems with solution fall 2014




Question;For the problems that follow you must follow the format listed below in order to receive credit for the problem. You will note that it includes the null hypothesis, the alternative hypothesis, calculation of the experimental t value or P-value, the decision rule and the conclusion drawn.H0: Write the null hypothesis hereH1: Write the alternative hypothesis hereDecision Rule: Write here what would lead to the rejection of H0 --- remember the appropriate sign or signs are neededCalculations: Determine the experimental statistic hereConclusion: Write here the conclusion and why that particular conclusion was drawn1. A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score does not change after completing a formal logic course.AFTER 74 83 75 80 84 63 93 84 91BEFORE 73 77 70 77 74 67 95 83 842. The skid properties of regular tires have been tested and a mean skid distance of 155 feet has been established for standardized conditions. A new, more expensive tire has been developed and tests on a sample of 20 new tires yield a mean skid distance of 150 feet with a standard deviation of 07 feet. Because of the cost involved, the new tires will be purchased only if it can be shown at the 99% confidence level that they skid less than the regular tires. Based on this sample, will the new tires be purchased?3. At Kellogs Cereal Company the quality control manager claims that cartons filled by the newest machine have more cereal in them than cartons filled by the oldest machine. Samples taken from each machine, which operates independent of each other, yielded the following results:Machine 1 Machine 2Sample size 25 36Sample mean 32.1 oz 30.9 ozSample s 2.2 oz 1.98 ozAt the 0.05 level of significance, test the claim that the population mean for the newest machine (machine #1) is larger than the population mean for the oldest machine (machine 2).4. Based on the sample data (data are in inches) below, what can you conclude about the heights of men and women? Do the sample data suggest that men and women have the same mean height? Do the results agree with your knowledge of the heights of men and women? Assume a 0.05 significance level.Men 72.0 71.6 68.7 65.9 76.4Women 63.9 67.1 63.2 64.7 70.45. In low-speed crash tests of five SMART cars, the repair costs were computed for a factory-authorized repair center and an independent repair facility. The results are listed in the accompanying table.a. Is there sufficient evidence to support the claim that the independent center has lower repair costs? Use a 0.05 significance level.Authorized repair center $797 $571 $904 $1,147 $418Independent repair center $523 $488 $875 $911 $297


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