1. IE241 Problems 2

2. 1. In a poll taken among college students, 46 of 200 fraternity men favored a certain proposition, whereas 51 of 300 nonfraternity men favored it. Is there a real difference of opinion on this proposition?

3. 2. A test of 200 youths and 500 adults showed that 50 of the youths and 60 of the adults were poor drivers. Test the claim that the youth percentage of poor drivers is 10 percentage points higher than the adult percentage of poor drivers vs the claim that the youth percentage is more than 10 percentage points higher than the adult percentage.

4. 3. Two sets of 100 children each were taught to read by two different methods. After the instruction was over, each class took a reading test. For group A, the mean = 73.4 and the standard deviation = 8. For group B, the mean = 70.3 and the standard deviation = 10. Is there a difference between the two teaching methods?

5. 4.The number of individuals possessing the four blood types should be in the proportions: q 2 :p 2 +2pq:r 2 +2qr:2pr Given the observed frequencies, 180, 360, 132, 98, test for compatibility with p =.4, q =.4, r =.2.

6. 5. A new drug claims to be effective in curing colds. In an experiment on 164 people with colds, half were given the drug, and half, a placebo. Is the drug effective if the results were: HelpedHarmedNo effectTotal Drug 52102082 Placebo 44122682 Total 962246164

7. 6. Given that X is normally distributed, assume that the results of a sample of size 20 had a mean = 42 and s = 5. (a) Test the hypothesis that σ = 8. (b) Test the hypothesis that μ = 45.

8. 7. Two random samples are taken from two normal populations. Test the hypothesis that μ 1 = μ 2. Make sure that your test is valid. Sample 1Sample 2 n1012 mean2024 s56

9. 8. The following data give the protein gains of 20 rats. Half of them received their protein from raw peanuts and the other half, from roasted peanuts. Test to see whether roasting the peanuts had any effect on protein value. Is the test valid? Mea n Varianc e raw57.931.21 roasted55.821.07

10. 9. The following table gives data on the hardness of wood stored outside and inside. Test to see if the variability of hardness is affected by weathering. OutsideInside n40100 mean117132 s 14.89716.589

11. 10. Coated and uncoated steel pipes were tested for corrosion effects. The results are shown in the table below. Test the hypothesis that the difference between the means = 0. Then find the 95% confidence interval for the difference between the means. PipesnMeanVariance Coated2044.45 88.47 Uncoated2051.4 104.88

12. 11. A thousand people were classified by gender and color-blindness, with results as shown below. Are gender and color-blindness independent? MaleFemaleTotal Normal 442 514 956 Color-blind 38 6 44 Total 480 520 1000

13. 12. Twelve pairs of runners have been matched with respect to ability. Each member of a pair is given a pill before the race. One member of each pair is given a stimulant in his pill, but the other is not. Each runner runs a race and the times are recorded below. Is the stimulant effective? Compute a 95% confidence interval for the difference between the means. Pair123456789101112 Stimulan t 64626361 596264656263 No Stim646365626361626665646563

14. 13. In an industrial experiment, the time needed to do a job by method 1 was compared with the time needed to the same job by method 2. Given the times shown below, is method 1 better than method 2? If so, do a 95% confidence interval on the time difference. Method 1Method 2 mean53.755.375 variance1518 n3040

15. 13.