Question

You are investigating the difference in weight gain between female and male iguanas when they are both given a high protein diet for a week. Each iguana in the study is to be matched with another iguana of opposite sex, of similar age and size. From similar studies done in the past, you know that female iguanas, on average, put on 2.5 more pounds of weight than male iguanas do post-diet. These studies also indicate that the standard deviation of their difference in weight post-diet is 3 pounds Suppose it is reasonable to assume that the difference in weight gain between male and female iguanas post-diet is normal. Fourteen female and fourteen male iguanas have just finished going through this experiment, and their average difference in weight is to be measured.

(a) What is the correct notation for the statistic of interest?

(b) What is the mean of the sampling distribution of the sample mean difference in weight between the female and the male iguana post-diet?

(c) What is the standard deviation of the sampling distribution of the sample mean difference in weight between the female and male iguanas?

(d) What is the probability that the average weight gain of the male iguanas in the sample is greater than the average weight gain of the female iguanas?

Answer 1

a) The correct notation for statistic for interest is where d = female weight gain-male weight gain.

b) Given, female iguanas, on average, put on 2.5 more pounds of weight than male iguanas do post-diet. Therefore:

c) The standard deviation of the sampling distribution of the sample mean difference in weight between the female and male iguanas is:

d) The probability that the average weight gain of the male iguanas in the sample is greater than the average weight gain of the female iguanas means . Therefore: