Question

Heights of Fathers and their sons

Fathers Sons

6'0 5'9   

5'11   6'1

5'11 5'11

6'1 5'9

5'9 5'7

6'2 5'10

6'0 6'0

6'1 5'11

5'8 5'11

5'11 6'2

• Clearly organize your data in a table and graph it in a scatter plot (this can be hand written).

• Test to see if there is a linear correlation between the variables x and y (father height and son height) by finding the linear correlation coefficient r. (use a 0.05 significance level)

• Then find the regression equation and accurately draw and label it on your scatter plot.

• Use the regression equation to make a prediction about the population your data came from. For example, if a father’s height is 83” what is the predicted height of his son?

Answer 1

First we change the height of fathers and their sons in cms

a) Scatter Plot :

b) Correlation Coefficient :

The Calculation table is given below :

Testing of Correlation Coefficient at 5% Significance Level

Null Hypothesis

Alternative Hypothesis

Under H0, the test statistic is

Degrees of freedom: n-2 = 8

The critical value of t at 5% significance level, is +/-2.306

Since , t calculated falls between the critical values of t, we fail to reject the null hypothesis, and conclude that there is no linear correlation between the heights of fathers and their sons.

c) Regression Equation :

Scatter Plot :

Prediction If the Father's height is 8'3 ( = 251.46 cms) , then the predicted height of their son is

The predicted height of son will be 4'11