Question

P-Values In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation.

Using the data from Exercise 8 “Heights of Fathers and Sons,” the P-value is 0.963.

Short answer

The p-value equal to 0.963 is very high, indicating that there is a large probability that the linear correlation between the variables, the height of the father and the height of the first son, is by chance.

Thus, it can be concluded that there is insufficient evidence to conclude that there exists a linear correlation between the height of the father and the height of the first son.

Step-by-step solution

Given information

The p-value of the linear correlation between the height of the father and the height of the first son is equal to 0.963.

Interpret the p-value

The probability value that the computed value of r is by chance and there is no actual correlation between the two variables is determined by the p-value.

In this case, the P-value implies that the chance of getting the sample correlation value as extreme as the computed value is 96.3%, assuming that the heights of father and son are not linearly correlated.

State the conclusion

The conclusion is stated as per the following criteria:

• When the p-value is less than or equal to 5%, it indicates that there is a significant linear correlation between the two variables.

• When the p-value is greater than 5%, it indicates that there is no linear correlation between the two variables.

The p-value for the correlation between the heights of the father and the first son is equal to 0.963.

Moreover, the p-value is greater than 0.05.

Therefore, it can be concluded that there is insufficient evidence to conclude that there exists a linear correlation between the height of the father and the height of the first son.