Question

A researcher conducted a study to investigate the relationship between cigarette smoking and illness. The number of cigarettes smoked daily and the number of days absent from work in the last year due to illness was determined for 12 individuals employed at the company where the researcher works. The researcher found r = +.62, so r 2 = .38. The researcher used a non-directional hypothesis with an alpha of .05. Write a results section. Be sure to include all relevant information, such as the test statistic written in journal form.

Interpret the r ².

Answer 1

Correlation Coefficient r = +0.62

There is moderate positive linear relation between cigarette smoking and illness

$H0: \rho = 0$

$H1: \rho \neq 0$

The test statistic is

$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}} =\frac{0.62\sqrt{10}}{\sqrt{1-0.38}} =2.49$

df = n-2= 10

The P-Value is .0320

Since p value is less than significance level, Reject H0

Hence there is linear relation exists between between cigarette smoking and illness

Coefficient of Determination r² = 0.38

38% of the variation in number of days absent from work is explained by the variation in cigarette smoking