Question

A random sample of 5 college women was asked for their own heights and their mothers' heights. The researchers wanted to know whether the college women are taller on average than their mothers. The results (in inches) follow:

Pair	1	2	3	4	5
Daughter	66	65	66	66	70
Mother	61	63	63	60	67

Let d=d= daughter's height - mother's height, and let μdμd represent the average height difference of daughter-mother pairs.

1. What is the sample mean of height difference between daughters and mothers (i.e. d¯d¯)? [answer to 1 decimal place]

2. What is the sample standard deviation of height difference between daughters and mothers sdsd? [answer to 3 decimal places]

3. Compute the standard error of d¯d¯, i.e. s.e.(d¯)s.e.(d¯) [answer to 3 decimal places]

4. Compute the margin of error of the 90% paired confidence interval for μdμd. [answer to 3 decimal places]

5. The 90% paired confidence interval for μdμd is:
a. (2.234, 5.366)
b. (1.757, 5.843)
c. (0.419, 7.181)
d. (2.675, 4.925)
e. (1.044, 6.556)

6. Based on 90% paired confidence interval for μdμd, we can conclude that
a. one cannot make any comparison of daughters' and mothers' heights based on confidence interval
b. there is significant evidence that on the average daughters are shorter than their mothers
c. there is significant evidence that on the average daughters are taller than their mothers
d. there is no significant evidence that average height of daughters is different from the average height of their mothers

Answer 1

The sample mean of height difference

sample standard deviation of height difference

and sample size

So, standard error of is

The margin of error of the 90% paired confidence interval for μ_d is

The 90% paired confidence interval for μd is

ans-> a. (2.234, 5.366)

6. c. there is significant evidence that on the average daughters are taller than their mothers