Suppose you are analyzing the daily profit of two different onboard products. Yo

Question

Suppose you are analyzing the daily profit of two different onboard products. You have data for 100 days of sales for organic chips and data for 60 days of sales for a granola bar.

Part a: Assume the daily profit values for both products can be modeled with a normal distribution. Describe how you would test whether the mean daily profit of organic chips is different from the mean daily profit of the granola bar. State any assumptions.

Part b: Suppose that neither the daily profit value for organic chips nor the daily profit value for the granola bar can be adequately modeled with a normal distribution. Describe how you would test whether the mean daily profit of organic chips is different from the mean daily profit of the granola bar. State any assumptions.

Explanation / Answer

(a) We use here two sample independent t-test to test whether the mean daily profit of organic chips is different from the mean daily profit of the granola bar if assumptions of this test are satisfied.

Assumptions-

(i)The populations from which the samples have been drawn should be normally distributed.

(ii)The variance of the populations should be equal i.e. X2 = Y2 = 2, where 2 is unknown. This assumption can be tested by the F-test.

(iiiSamples have to be randomly drawn independent of each other.

(b) If neither the daily profit value for organic chips nor the daily profit value for the granola bar can be adequately modeled with a normal distribution i.e. assumption is not satisfied then we use Mann Whitney U test which is an non-parametric alternative to two sample independent t-test

Assumptions-

Ordinal or continuous dependent variable.

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