Question

In: Statistics and Probability

Conduct a regression and correlation hypothesis test (step 1 to 5) on the data below before...

Conduct a regression and correlation hypothesis test (step 1 to 5) on the data below before you answer each
question.
The number of fat calories and number of saturated fat grams for a random selection of nonbreakfast entrees
are shown below. Use a .05 level of significance.
y x
9 190
8 220
13 270
17 360
23 460
27 540
What is the p value for this problem?

Solutions

Expert Solution

null hypothesis: Ho:           ρ'= 0
Alternate Hypothesis: Ha: ρ≠ 0
0.05 level,two tail test and n-2= 4 df, critical t=2.7764 (from excel:tinv(0.05,4)
Decision rule: reject Ho if absolute value of test statistic |t|>2.7764
correlation r='Sxy/(√Sxx*Syy) = 0.9927
test stat t= r*(√(n-2)/(1-r2))= 16.506
P value    = 0.0001 (from excel:tdist(16.506,4,2)
since p value is less than significance level , we reject null hypothesis

And conclude that there is significant linear association between number of fat calories and number of saturated fat grams


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