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  α = 0.05, that the hamburgers from the two chains have a different number of Calories? Use an independent t-test. df = smaller of n₁ - 1 or n₂ - 1.

	Chain A	Chain B
Sample Size	5	9
Sample Mean	230 Cal	285 Cal
Sample SD	23 Cal	29 Cal

		A) No, because the test value –0.28 is inside the noncritical region.
		B) Yes, because the test value –0.28 is inside the noncritical region
		C) Yes, because the test value –3.90 is outside the noncritical region
		D) No, because the test value –1.26 is inside the noncritical region

Answer 1

The test hypotheses are

Here are the population means of populations 1 and 2 respectively.

Here, the sample means are . The sample standard deviations are

The level of significance is . The sample sizes are . The degrees of freedom is .

Since the population standard deviations are not known, we use t-distribution.

Thus the test statistic is

The critical value is

Since , the test statistic is outside the noncritical (inside the critical) region, we reject the null hypothesis.

Correct choice is (C).