Question

1.The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 8 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 8 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is 7.19 and the standard deviation of the differences is 17.7487. Calculate a 90% confidence interval to estimate the average difference in scores between the two courses.

a.(4.6987, 19.0787) b.(5.2954, 9.0846) c.(-4.4789, 18.8589) d.(0.9149, 13.4651) e.(-4.6987, 19.0787)

2.In a packing plant, one of the machines packs jars into a box. A sales rep for a packing machine manufacturer comes into the plant saying that a new machine he is selling will pack the jars faster than the old machine. To test this claim, each machine is timed for how long it takes to pack 10 cartons of jars at randomly chosen times. Given a 99% confidence interval of (-6.84, -1.71) for the true difference in average times to pack the jars (old machine - new machine), what can you conclude from this interval?

a.We are 99% confident that the average packing time of the old machine is greater than the new machine. The sales rep appears to be correct.

b.We are 99% confident that the average packing time of the new machine is greater than the old machine. The sales rep does not appear to be telling the truth.

c.There is no significant difference between the average packing times of the two machines. The sales rep does not appear to be telling the truth.

d.We are 99% confident that the difference between the two sample means falls within the interval.

3.Suppose that you are the director of table game operations at a large casino, known especially for its poker room. You are interested in determining the average number of hands the casino should expect per hour during peak hours in the poker room. You monitor the number of hands over the next week and given a random sample of 20 hours, you see that on average 197.3 hands are played per hour, with a standard deviation of 8.21 hands and you calculated a 90% confidence interval to be (194.1, 200.5). Your manager believes the true mean is 241.4. Which of the following is the best conclusion?

a.We are 90% confident that the average number of hands played per hour is greater than 241.4.

b.We are 90% confident that the average number of hands played per hour is less than 241.4.

c.The average number of hands played per hour is not significantly different from 241.4

Answer 1

solution Given 77-19 S.D=17.7487 n=8 df = n-1 tal2, df = 1.89457 c.I = ūt to, idt * Slim 37.19 £ 1-8945 * 1.7487 = 7.19 € 11.886 = (4.6986600, 19.0787) 21-4.6987, 19.0787) 2 we are 99% confident that the average packing time of the new machine is greatu Than The old machine The salds rep does not apper to be telling the truth. per hour is not ③ the average number of hands played sigmiffently different from 241.48