Question

The addition of bran to the porridge has been reported in increasing the sales to the hospitals by the Sales and Marketing Manager, Pakistan region of Quaker Chemicals Pvt Ltd. Several different bran preparations are available, and the Manager wants to test the efficiency of two of them, since favorable claims have been made for each by the clinicians. Among the consequences of administering bran that requires testing is the transit time through the alimentary canal in human body. Alimentary canal is a system within humans and other animals which takes in food, digests it to extract and absorb energy and nutrients, and expels the remaining waste. The clinicians and the Sales Manager wonder whether transit time would be shorter if bran is given in the same dosage in three meals during the day (Treatment 1) or in one meal (Treatment 2) to the same patients. A random sample of patients with disease of comparable severity and aged 20-44 is chosen and the two treatments are administered on two successive occasions. The alimentary transit times are measured and shown as in Table 1.

Patient	Treatment 1 Transit Time (minutes)	Treatment 2 Transit Time (minutes)
1	63	55
2	54	62
3	79	108
4	68	77
5	87	83
6	84	78
7	92	79
8	57	94
9	66	69
10	53	66

Construct the 99% confidence interval estimate for the difference in the population means based on Table 1.

Answer 1

Solution:

Where:

is the mean of the differences

is the standard deviation of the differences