This Is The Original Question Test the hypothesis test that

This Is The Original Question

Test the hypothesis test that the average pizza delivery man in New York is more than DC by comparing the sample z-score to the critical z-score at a 0.05 significance level. Use the information listed below.

NY = sample 40, sample mean $52,378, standard deviation $6,812

DC = sample 42, sample mean $48,773, standard deviation $7,514

The Answer

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(1) H0: u₁ - u₂ < 0

     H1: u₁ - u₂ > 0

(2) calculate standard error: (6,812 / 40)² + (7,514 / 42)² = 1,582.52

(3) calculate the difference between sample means = 52,378 - 48,773 = 3,605

(4) calculate sample z-score = 3,605 - 0 / 1,582.52 = 2.28

(5) answer: sample z-score 2.28 is greater than critical z-score 1.64 thus we reject the null and conclude that their is sufficient evidence to support the claim.

Class, verify the answer above by comparing the p-value to the level of significance of 0.05.

Solution

As this is a right tailed test, then using table/technology, the right tailed area of z = 2.28 is

P = 0.011303844

As P < 0.05, then we REJECT THE NULL HYPOTHESIS.

There is significant evidence that the average pizza delivery man in New York is more than DC. [CONCLUSION]