A) Two arthroscopic surgeries were compared among patientssuffering from osteoarthritis who had at least moderate knee pain.The lavage type has the joint flushed with fluid and no instrumentis used to remove tissue; the debridement type has the jointflushed with fluid and an instrument is used to remove tissue. Kneepain scores, ranging from 0 to 100 with higher scores indicatingsevere pain, were obtained for patients randomly assigned to thetwo groups after the surgery and the results are given below:

------------Sameple Size--------Sample Mean-------SampleStandard Deviation

Lavage 11 59 24

Debridment 13 49 23

Determine a 95% confidence interval for the difference betweenthe mean knee pain score for the lavage group and that for thedebridement group

B) A test of abstract reasoning is given to a random sample of10 students before and after completing a formal logic course. Theresults are shown below.

Before----------After

71 71

81 86

85 82

67 75

92 95

71 66

61 67

78 81

64 71

80 88

Determine a 95% confidence interval for the difference betweenthe mean score after completing the course and the mean scorebefore completing the course

C) The quality control officer collects a random sample of 100yardsticks from the day's production run. The sample mean is 36inches. The population standard deviation for that day’s productionis σ =1 inches.

1)Find a 99% confidence interval for the mean length of allyardsticks made that day

2)The margin of error associated with the 99% confidenceinterval for the mean length of all yardsticks made that day is

3)You decide that margin of error in previous question is toolarge, and you want it to be at most 0.1 inches, what is theminimum sample size in order to obtain this margin of error with aconfidence level of 99%?