Question

11. 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? Assume that population variances are unequal. Chain A Chain B Sample size Sample mean Sample standard deviation 230 calories 23 ccalories 285 calories 29 calories Hypotheses: Critical value(s): Test stat calculations: Decision: Conclusion:

Answer 1

H₀: $\mu1 = \mu2$

H₁: $\mu1 \neq \mu2$

df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

= ((23)^2/5 + (29)^2/9)^2/(((23)^2/5)^2/4 + ((29)^2/9)^2/8)

= 10

At alpha = 0.05, the critical values are +/-t_0.025,10 = +/- 2.228

The test statistic t = ($\bar x1 - \bar x2$)/sqrt(s1^2/n1 + s2^2/n2)

= (230 - 285)/sqrt((23)^2/5 + (29)^2/9)

= -3.896

Since the test statistic value is less than the lower critical value (-3.896 < -2. 228), so we should reject the null hypothesis.

At alpha = 0.05, we can conclude that the hamburgers from the two chains have a different number of calories.