In a simple random sample of 250 father-son pairs taken from a large population of such pairs, the mean height of the fathers is 68.5 inches and the SD is 2.5 inches; the mean height of the sons is 69 inches and the SD is 3 inches; the correlation between the heights of the fathers and sons is 0.5.

Question

In the population, are the sons taller than their fathers, on average? Or is this just chance variation?
The SE of the mean difference between heights of fathers and sons in the sample is closest to 0.176.

Problem 1.
Which of the following most closely represents the result of the test?
- The result is not statistically significant, so we conclude that it is due to chance variation.
- The result is not statistically significant, so we conclude that the sons are taller than their fathers, on average.
- The result is highly statistically significant, so we conclude that the sons are taller than their fathers, on average.
- The result is highly statistically significant, so we conclude that it is due to chance variation

Answer 1

Z = (mean1 - mean2)/standard error (SE) of difference between means

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Are you using two-tailed test or one-tailed test?

You can eliminate some choices: significance = not chance and non-significance = chance.

What criterion are you using to reject your null hypothesis? P≤.05? P≤.01?

Answer 2

0.5

Answer 3

Building on above answer from PsyDAG, when you run the calculation for Z and check the normal distribution table, you get get a p value of 0.22%, which is highly statistically significant, so we conclude that sons are taller, on average, than their dads.

Answer 4

Being P so small, it must be the other answer?? right???