Robbie predicts that eating at Jimmy John’s has an effect on mean cholesterol, b

Question

Robbie predicts that eating at Jimmy John’s has an effect on mean cholesterol, but he doesn’t have a prediction for the direction of the effect. Robbie’s sample of 18 Jimmy John’s customers have an average total cholesterol of 224 mg/dL, while the general population has a slightly lower mean cholesterol ( = 207 mg/dL, = 34). First, calculate the z statistic for this nondirectional hypothesis. Second, using the well-known critical values for ­z-scores at = .05, determine whether Robbie will reject H0. Now that you know what Robbie will conclude based on his data, I tell you the capital-T Truth that eating at Jimmy John’s does not have a systematic effect on cholesterol levels. Select which scenario below describes Robbie’s decision based on his data and the Truth.

Type I error

Correctly retaining H0

Type II error

Correctly rejecting H0

Explanation / Answer

Hypothesis testing:

H0: no effect of Jimmy John's (mean cholestrol for both are equal)

Ha: there is difference

this is 2 sided 1 sample z test with Normality assumption.

z-score = (x-Mu) /(sigma/sqrt(n)) = (224-207)/(34/sqrt(18)) = 2.12

p-value = 0.03 (=2*(1-NORMSDIST(2.12))) <0.05;

we reject H0 and conclude that there is significant effect of Jimmy John's on Cholestrol.

next part:

given that actually there is no effect of Jimmy John's on Cholestrol and if we reject this fact then we are committing Type I error.

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