Question

You conduct a study to investigate the relationship between diet soda drinkers and obesity. You ask 30 people two questions: 1) “How many diet sodas did you drink in the past week?” and 2) “How many pounds overweight are you?” You compute a Pearson correlation between the answers to your two questions, and find that r = .41.

Answer 1

here, we conduct a study to investigate the relationship between diet soda drinkers and obesity.

given data are:-

sample size (n) = 30

correlation coefficient (r) = 0.41

we will perform a hypothesis test to check whether there is a significant relationship between the two variables.

hypothesis:-

where corresponds to the population correlation.

test statistic:-

degrees of freedom = (n-2) = (30-2) = 28

critical value of t for alpha = 0.05,df = 28, both tailed test :-

[ from t distribution table]

[ as nothing is mentioned i am using alpha = 0.05 ]

decision:-

so,we reject the null hypothesis.

conclusion:-

hence,we conclude that,

there is a significant relationship between diet soda drinkers and obesity .

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