Chapter 10, Problem 1CQQ

The following exercises are based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

1. Conclusion The linear correlation coefficient r is found to be 0.499, the P-value is 0.393, and the critical values for a 0.05 significance level are ±0.878. What should you conclude?

To determine

To conclude: About the linear correlationbetween the numbers of enrolled students and numbers of burglaries.

Answer to Problem 1CQQ

There is no sufficient evidence to support the claim that there is a linear correlation between the numbers of enrolled students and numbers of burglaries.

Explanation of Solution

Given info:

The data shows that the numbers of enrolled students (in thousands) and the numbers of burglaries. The correlation value is 0.499, the critical values at 0.05 level of significance for r is $\pm 0.878$ and P-value for r is 0.393.

Calculation:

The hypotheses are given below:

Null hypothesis:

$H_0:\rho =0$

That is, there is no linear correlation betweenthe numbers of enrolled students and the numbers of burglaries.

Alternative hypothesis:

$H_1:\rho \ne 0$

That is, there is a linear correlation between the numbers of enrolled students and the numbers of burglaries.

Conclusion:

The P-value is 0.393 and the level of significance is 0.05.

Here, the P-value is greater than the level of significance.

Hence, the null hypothesis isnot rejected. That is, there is no linear correlation betweenthe numbers of enrolled students and the numbers of burglaries.

The critical value is ±0.878.

Here, the correlation value is 0.499 which lies between the critical values.

Hence, the null hypothesis isnot rejected.

Thus, there is nosufficient evidence to support the claim that there is a linear correlation betweenthe numbers of enrolled students and the numbers of burglaries.