A reporter bought hamburgers at randomly selected stores of two different restau

Question

A reporter bought hamburgers at randomly selected stores of two different restaurant chains, and had the number of Calories in each hamburger measured. Can the reporter conclude, at ? = 0.05 , that the hamburgers from the two chains have a different number of Calories?

Chain A Chain B

Sample size 5 9

Sample mean 280 Cal 335 Cal

Standard deviation 19 Cal 27 Cal

a. No, because the test value –0.36 is inside the noncritical region ?2.306 < t <2.306

b. Yes, because the test value –0.36 is inside the noncritical region ?2.776 < t <2.776

c. Yes, because the test value –4.44 is outside the noncritical region ?2.776 < t <2.776

d. No, because the test value –1.42 is inside the noncritical region ?2.306 < t <2.306

Explanation / Answer

t = (Sample mean 1 - sample mean 2) / sqrt( (Sample 1 variance / sample 1 size) + (Sample 2 variance / sample 2 size))

t = (280-335) / sqrt( (19^2 / 5) + (27^2)/9)

t = -55 / 12.38

t = -4.44

Thus, option C

Yes, because the test value –4.44 is outside the noncritical region ?2.776 < t <2.776

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