College Women/ Mothers Height Question

Question

Are college women are taller on average than their mothers. The results (in inches) were as follows:

Pair             1  2   3   4  5
Daughter    66 64 64 69 66
Mother       66 62 65 66 63

a. Define the parameter of interest in this situation.
b. Find a 95% confidence interval for the parameter you defined in part (a).
c. Using the interval in part (b), write a sentence or two about the relationship between women students’ heights and their mothers’ heights for the population. Your explanation should be written to be understood by someone with no training in statistics.
d. Explain two different things that the researchers could have done to obtain a narrower interval than the one you found in part (b).

Answer 1

a. The parameter of interest is the population mean difference between the heights of mother-daughter pair

b. find the difference between each pair (daughter height-mother height). Calculate the mean and standard deviation of these differences to get sample mean difference d-bar, and the sample standard deviation sd.

daughter 66 64 64 69 66

mother 66 62 65 66 63

difference 0 2 -1 3 3 d-bar=1.4, sd=1.8166

Use the following formula to get the t interval: d-bar +/- (t*. sd.sqrt n).

-t* can be read from the t table for area .025 in one tail and with degrees of freedom (n-1)=4, here n=5 as there are 5 pairs=2.776

lower=1.4-(2.776*1.8166/sqrt 5) =-0.8552

upper=1.4+(2.776*1.8166/sqrt 5) =3.6552

c. the 95% confidence interval [-0.8552,3.6552] contains zero. So we can say with 95% confidence that the mean population difference between the heights of mother daughter pair is zero. Or that on an average , college women have the same heights as their mothers.

d. to get a narrower interval-1) reduce the level of confidence. for example a 90% confidence interval will be narrower than 95%. 20 increase the sample size, that is, number of pairs in the data set.

Hope this is helpful.