11 14 03 252x0323 Page layout view ECO252 QBA2 SECOND HOUR EXAM October 30 2003 Name Hour of Class Registered Circle 11am 12 30pm Note the following 1 You will be penalized if you do not compute the sample variance of the d column in question 20 so you might want to do it now 2 This test is normed on 50 points but there are 74 points possible including the take home You may not finish the exam and might want to skip some questions 3 A table identifying methods for comparing 2 samples is at the end of the exam I 53 points Do all the following 2points each unless noted otherwise 1 A manufacturer revises a manufacturing process and finds a fall in the defect rate of 5 4 a b c d 2 The fall in defects is statistically significant because 5 is larger than 4 The fall in defects is statistically significant because the confidence interval supports H0 The fall in defects is not statistically significant because 4 is smaller than 5 The fall in defects is not statistically significant because the confidence interval would lead us to reject H0 If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2 the appropriate test to use is a the z test 2 b the test c both of the above d none of the above TABLE 12 14 Recent studies have found that American children are more obese than in the past The amount of time children spend watching television has received much of the blame A survey of 100 ten year olds revealed the following with regards to weights and average number of hours a day spent watching television We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1 level of significance Weights More than 10 lbs overweight Within 10 lbs of normal weight More than 10 lbs underweight Total 3 0 3 1 20 10 31 TV Hours 3 6 9 15 5 29 6 20 15 5 40 Total Referring to Table 12 14 if there is no connection between weights and average number of hours spent watching TV we should expect how many children to be spending 3 6 hours on average watching TV and are more than 10 lbs underweight a 5 b 5 8 c 6 2 d 8 30 50 20 100 10 24 03 252x0323 4 Turn in your computer output from computer problem 1 only tucked inside this exam paper 3 points 2 point penalty for not handing this in MTB TwoT 90 0 educ sex SUBC Alternative 1 Two Sample T Test and CI EDUC SEX Two sample T for EDUC SEX Female Male N 788 651 Mean 13 19 13 28 StDev 3 03 2 85 SE Mean 0 11 0 11 Difference mu Female mu Male Estimate for difference 0 091 90 upper bound for difference 0 108 T Test of difference 0 vs T Value 0 58 P Value 0 280 DF 1412 The computer output above refers to a test very much like the Minitab test you ran of two independent samples The major difference is that 1439 numbers appear in column 1 labeled EDUC which give number of years of education completed and the computer sorted them by gender using the words female and male in column 5 labeled SEX The variable x F can thus refer to an imaginary column of female education figures and x M to in imaginary column of male education figures Call this the GSSEduc output 5 Referring to the GSSEduc output and using the rules taught in class the null hypothesis that was tested is a H0 F M 0 b H0 F M 0 c H0 F M 0 d H0 F M 0 6 Referring to the GSSEduc output we can conclude doing no more calculations that for the particular population that was sampled a At the 10 level there is sufficient evidence that women had fewer years of education than men b At the 10 level there is a difference between the years of education gotten by men and women c At the 10 there is insufficient evidence that the average men s education level is higher than the women s d At the 10 level there is sufficient evidence to conclude that there is no difference between men s and women s education level 7 Referring to the GSSEduc output the most commonly used methods to find degrees of freedom are i to calculate df n1 n 2 2 788 651 2 1437 or ii to say that since we have large sample to use z which is equivalent to saying that the degrees of freedom are infinite yet the computer claims df 1412 Explain briefly what the computer probably did and assumed to get that number 2 10 24 03 252x0323 8 Wonnacott and Wonnacott A small piece of hose in the cooling system of a new engine has a lifetime that varies normally following the Normal distribution around a mean of 18 months with a standard deviation of 4 months The first maintenance check occurs at 12 months What is the probability that the hose will wear out before the maintenance check This is the same as the per cent of hoses that will wear out before the first maintenance check Make a diagram 9 In problem 8 above the manufacturer decides that too much money is being spent on maintenance checks If the manufacturer is willing to accept having 20 of hoses wear out before the fist maintenance check how many months to the nearest 100 th of a month can the manufacturer wait until the check This is the same as finding the 20 th percentile of the distribution 10 The t test for the difference between the means of 2 independent populations assumes that the respective a sample sizes are equal b sample variances are equal c populations are approximately normal d all of the above TABLE 10 3 The use of preservatives by food processors has become a controversial issue Suppose 2 preservatives are extensively tested and determined safe for use in meats A processor wants to compare the preservatives for their effects on retarding spoilage Suppose 15 cuts of fresh meat are treated with preservative A and 15 are treated with preservative B and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat The results are summarized in the table below Preservative A x A 106 4 hours s A 10 3 hours Preservative B xA sB 96 54 hours 13 4 hours 11 Referring to Table 10 3 state the test statistic for determining if the population variance for preservative B is larger than the population variance for preservative A a F 3 100 b F 1 300 c F 1 693 d F 0 591 3 10 24 03 252x0323 12 Referring to Table 10 3 what assumptions are necessary for a comparison of the population variances to be valid a …
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