A service station owner believes that equal numbers of customers prefer to buy gasoline on every day of the week. A manager at the service station disagrees with the owner and claimed that the number of customers who prefer to buy gasoline on each day of the week varies. Test the manager's claim using 0.10 level of significance. The owner surveyed 739 customers over a period of time to record each customer's preferred day of the week. Here's what he found. Preferred Day to Buy Gasoline Monday Tuesday Wednesday Thursday Friday Saturday | Sunday Number 103 103 126 103 111 96 Total-739 H: PM PT = Pw PR Pr = Ps Ps H: There is some differences amongst the probabilities. 97 Day of Week Observed (o) Expected (e) (0-e) (0-6)² e Monday 103 739/7-105.71 -2.57 6.6122 .0626 Tuesday 103 105.71 -2.57 6.6122 .0626 Wednesday 126 105.71 20.429 417.33 3.953 Thursday 103 105.71 -2.57 6.6122 .0626 Friday 111 105.71 5.4286 29.469 .27914 Saturday 96 105.71 Sunday 97 105.71 -9.571 91.612 -9.571 73.469 .86777 .69592 1-5.984 Test Statistic Degrees of freedom-7-1-6 (number of classes-1) Critical Value: x²: 10.645 From x² Table p-value: 0.4250 on Calculator 0.4250>0.10 Fail to Reject Conclusion: At the .10 level of significance the evidence does not support the manager's claim that the number of customers who prefer to buy gasoline on each day of the week varies. A soft drink company is interested in knowing whether there is a relationship between cola preference and age. A random sample of 800 people is chosen for a taste test. The results of the study are found in the following table. Is there sufficient evidence at the 0.005 level of significance to lead you to believe that there is an association between cola preference and age? Observed Sample of 800 People Cola A Cola B Cola C Total 15-29 94 102 105 301 30-44 99 97 86 282 45-59 68 73 76 217 Total 261 272 267 800 Expected Values CURT CURB CON Total 15.20 (301)(261/800 (3012721/800 (30132671/800 301 Conclusion: There is not sufficient evidence at the 0.01 level of significance to support the claim that students SAT scores increase by a mean of more than 60 points after completing the SAT prep courses. University officials hope that changes they have made have improved the retention rate. In 2010, a sample of 1926 freshmen showed that 1400 returned as sophomores. In 2011, 1508 of 2011 freshmen sampled returned as sophomores. Determine if there is sufficient evidence at the 0.05 level to say that the retention rate has improved. H: P₁ ≥ Pz 1508 P₁ = .73 P₂ = = .75 +1400+1505 2905 .74 +2 1926+2011 3937 (Fi-Fi)-(P1−P₂) √B(1-5)C Critical Value: invNorm(.05): -1.64 (73-75)-0 75(1-75)(2011) -1.43 Test Statistic p-value: 0.0505 or on table at -1.64 0.0505>0.05 Fail to Reject Conclusion: There is sufficient evidence at the 0.05 level of significance to support the university's claim that the retention rate improved between 2010 and 2011. A service station owner believes that equal numbers of customers prefer to buy gasoline on every day of the week. A manager at the service station disagrees with the owner and claimed that the number of customers who prefer to buy gasoline on each day of the week varies. Test the manager's claim using 0.10 level of significance. The owner surveyed 739 customers over a period of time to record each customer's preferred day of the week. Here's what he found. Monday Tuesday Wednesday Thursday Friday Saturday Sunday 111 Preferred Day to Buy Gasoline Number 103 103 126 103 Total-739 H: PM = PT = Pw = PR = PF = Ps = Ps H: There is some difference we 96 97 7 of 9