Question

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The Economist collects data each year on the price of a Big Mac in various countries around the world. A sample of McDonald's restaurants in Europe in July 2016 resulted in the following Big Mac prices (after conversion to U.S. dollars). 4.42 3.15 2.40 4.61 3.98 3.77 4.32 3.35 4.50 3.86 4.14 3.70 The mean price of a Big Mac in the U.S. in July 2016 was $5.04. For purposes of this exercise, you can assume it is reasonable to regard the sample as representative of European McDonald's restaurants. Does the sample provide convincing evidence that the mean July 2016 price of a Big Mac in Europe is less than the reported U.S. price? Test the relevant hypotheses using a = 0.05. (Hint: See Example 12.12.) State the appropriate null and alternative hypotheses. Ho: 4 < 5.04 Hau > 5.04 . Ho: 4 = 5.04 He: 4 < 5.04 O Hou > 5.04 H: 4 < 5.04 Ho: = 5.04 Ha: 4 > 5.04 O Hp: = 5.04 He: 4 + 5.04 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your p-value to three decimal places.) t = 1.8 X P-value = .050 State the conclusion in the problem context. We reject H. We have convincing evidence that the mean July 2016 price of a Big Mac in Europe is less than the reported U.S. price. We fail to reject H. We have convincing evidence that the mean July 2016 price of a Big Mac in Europe is less than the reported U.S. price. We fail to reject Ho. We do not have convincing evidence that the mean July 2016 price of a Big Mac in Europe is less than the reported U.S. price. . We reject H. We do not have convincing evidence that the mean July 2016 price of a Big Mac in Europe is less than the reported U.S. price.

Answer 1

The statistical software output for this problem is:

One sample T hypothesis test: V: Mean of variable Ho : = 5.04 HA: < 5.04 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat P-value Data 3.85 0.18501433 11 -6.4319342 <0.0001

Hence,

t = -6.43

P-value = 0.000

Conclusion: Option A is correct.