A researcher was interested in knowing whether the mean weight of the second baby is higher, lower, or about the same as the mean weight of the first baby for women who have at least two children. She selected a representative sample of 40 women who had at least two children and asked them for the weights of the oldest two at birth. She found that the mean of the differences (first - second) was 5 ounces, and the standard deviation for the differences was 7 ounces.

a. Why was the researcher's study design better than taking independent samples of mothers and asking the first sample about the weight of their first baby and the second sample about the weight of their second baby?
b. Define the parameter for interest. Use appropriate notation.
c. Write the mean of 5 ounces and the standard deviation of 7 ounces using appropriate statistical notation.
d. Find a 90% confidence interval for the parameter that you define in part (b). Write a sentence or two interpreting the interval.
e. Draw a picture of the confidence interval you found in part (d). Using this picture, would you conclude that the mean birth weights for the population are likely to differ?