4. In a recent study of the effectiveness of popular diet plans, subjects were g

Question

4. In a recent study of the effectiveness of popular diet plans, subjects were given a numerical score of how well they adhered to the diet, as well as having their weight loss measured. For the 43 subjects who completed the study, the correlation coefficient between adherence score and weight loss turned out to equal .233. Conduct a significance test of whether this sample correlation coefficient is significantly greater than 0. Report the null and alternative hypotheses, test statistic, and p-value. Also write a sentence summarizing your conclusion.

Explanation / Answer

Given that   n = 43   r = 0.233

The null hypothesis is given by

Ho : the sample co relation is equal to zero i.e., = 0

Against the alternative hypothesis

H1 : the sample co relation is equal to zero i.e., > 0

The test statistic is given by

t = r*n-2/1-r2 (n-2)

t = (0.233)*43-2/1-(0.233)2

tcal =1.1228

the table value at 41 degrees of freedom is ttab =1.684

therefore tcal < ttab we accept the null hypothesis i.e., the sample correlation is equal to zero

the value of p is 0.06633670

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.