Question

McDonald’s is claiming that their grilled chicken sandwich has fewer calories than Burger King’s grilled chicken sandwich. In a sample of 15 sandwiches from McDonald’s, the mean calories per sandwich is 425 with a standard deviation of 8.1 calories. In a sample of 15 sandwiches from Burger King, the mean calories per sandwich is 445 with a standard deviation of 6.2 calories. Using α = 0.05, can McDonald’s claim their sandwiches have fewer calories?

Answer 1

Given that,

For McDonald's : n1 = 15, x1-bar = 425 and s1 = 8.1 calories

For Burger King's : n2 = 15, x2-bar = 445 and s2 = 6.2 calories

The null and alternative hypotheses are,

H0 : μ1 = μ2

Ha : μ1 < μ2

This hypothesis test is left-tailed.

Using TI-83 plus calculator we get,

Test statistic = t = -7.594

p-value = 0.0000

Since, p-value is less than significance level of α = 0.05, we should reject the null hypothesis.

Conclusion : There is sufficient evidence to support the McDonald's claim that their grilled chicken sandwich has fewer calories than Burger King’s grilled chicken sandwich.

Answer : Yes