A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 28 dieters, are chosen for the study, Group A is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day. Group B is required
follow the same
diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 11.1 pounds with a
standard deviation of 2.7 pounds. The members of Group B had lost a mean of 10.5 pounds with a standard deviation of 1.7 pounds during the same time period.
Assume that the population variances are not the same. Construct a 90 % confidence interval to estimate the true difference between the mean amounts of weight
lost by dieters who supplement with calcium and those who do not. Let Population 1 be the amount of weight lost by Group A, who took a 500 mg supplement of
calcium each day, and let Population 2 be the amount of weight lost by Group B, who did not take a calcium supplement. Round the endpoints of the interval to one
decimal place, if necessary.