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 | 65 | 68 | 67 | 66 | 63 |
Mother | 65 | 65 | 67 | 66 | 66 |
Let d=d= daughter's height - mother's height, and let μdμd represent the average height difference of daughter-mother pairs.
What is the sample mean of height difference between daughters and mothers (i.e. d¯d¯)? [answer to 1 decimal place]
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What is the sample standard deviation of height difference between daughters and mothers sdsd? [answer to 3 decimal places]
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Compute the standard error of d¯d¯, i.e. s.e.(d¯)s.e.(d¯) [answer to 3 decimal places]
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Compute the margin of error of the 90% paired confidence interval for μdμd. [answer to 3 decimal places]
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The 90% paired confidence interval for μdμd is:
(-1.452, 1.452)
(-2.021, 2.021)
(-4.365, 4.365)
(-3.559, 3.559)
(-2.638, 2.638)
Incorrect. | Tries 1/3 | Previous Tries |
Based on 90% paired confidence interval for μdμd, we can
conclude that
there is significant evidence that on the average daughters are
shorter than their mothers
there is no significant evidence that average height of daughters
is different from the average height of their mothers
there is significant evidence that on the average daughters are
taller than their mothers
one cannot make any comparison of daughters' and mothers' heights
based on confidence interval
Incorrect. | Tries 1/3 | Previous Tries |
Daughter's height | Mother's height | d |
65 | 65 | 0 |
68 | 65 | 3 |
67 | 67 | 0 |
66 | 66 | 0 |
63 | 66 | -3 |
Here
sample mean of difference
sample standard deviation of difference
and sample size
The standard error of is
Margin of error (ME)
Now,
The 90% paired confidence interval for μd is:
Based on 90% paired confidence interval for μd, we can conclude that :
there is no significant evidence that average height of daughters is different from the average height of their mothers
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