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?

a) Instead of taking independent samples of mothers and asking them first sample about the weight of their first baby and the second sample about the weight of their second baby this method is better. Because in the first type we do not know whether the mothers have two children and whether they remember weights etc. But in this the difference is ready made got form the eligible mothers

b) Parameter for interest is the difference in weights of two babies

mu1-mu2 where mu1 average weight of I baby while mu2 that of second

c) mu_d = 5oz. where mu_d represents the average difference in weight.

s_d std dev for difference = 7oz

d) Since sample size is >30, we can use Z critical value for confidence interval

Confidence interval = Mean ±1.645*std error

=[tex]5[/tex]±[tex]1.645*\frac{7}{\sqrt{40} }[/tex]

=(3.179, 6.821)

e) In number line the region between 3.179 and 6.821

Yes because if 0 is in the interval we can say there will not be difference. But 0 is not within this interval so would conclude that the mean birth weights for the population are likely to differ