Question

Suppose 50 married couples are asked to provide their ages. For all couples, the husband is exactly 2 years older than his wife. For example, a 50-year-old husband has a wife who is 48 years old. What is the best estimate of the correlation coefficient between the ages of husbands and their wives?

A) The correlation coefficient between the ages of husbands and wives is equal to 0.
B) No conclusions can be drawn without seeing a scatterplot of the data.
C) The correlation coefficient between the ages of husbands and wives is equal to 1.
D) The correlation coefficient between the ages of husbands and wives is equal to -1.

Answer 1

Suppose 50 married couples are asked to provide their ages.

For all couples, the husband is exactly 2 years older than his wife.

For example, a 50-year-old husband has a wife who is 48 years old.

Here as the age of husband increases, the age of the wife will be increased.

So we can say that the correlation is positive.because as the age of husband increases, the age of wife also increases.

Now we can see that as the age of husband is x then the age of wife is exactly x-2.

So the for all values of husband age value of wife age will be -2.

for example x: husbund age & y wife age

x: 22 30 36 40 48 50 60

y:- 20 28 34 38 46 48 58

So we can see that the correlation is exactly 1 because it is exactly the same pattern for x & y

Answer:- C) The correlation coefficient between the ages of husbands and wives is equal to 1.