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The Economist collects data each year on the price of a Big Mac in various countries around the world. The price of a Big Mac for a sample of McDonalds restaurants in Europe in May 2009 resulted in the following Big Mac prices (after conversion to U.S. dollars): 3.80 5.89 4.92 3.88 2.65 5.57 6.39 3.24 The mean price of a Big Mac in the U.S. in May 2009 was $3.57. For purposes of this exercise, assume it is reasonable to regard the sample as representative of European McDonalds restaurants. Does the sample provide convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price? Test the relevant hypotheses using α = .05. Assume a normal distribution of the data.

Respuesta :

Using the t-distribution, it is found that since the p-value of the test is 0.0428 < 0.05, the sample provides convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price.

At the null hypothesis, it is tested if the mean is the same, that is:

[tex]H_0: \mu = 3.57[/tex]

At the alternative hypothesis, it is tested if it is greater, that is:

[tex]H_1: \mu > 3.57[/tex]

We can find the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

  • [tex]\overline{x}[/tex] is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

For this problem, two of the values of the parameters are: [tex]n = 8, \mu = 3.57[/tex]

Additionally, with the help of a calculator: [tex]\overline{x} = 4.5225, s = 1.3468[/tex]

The value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{4.5225 - 3.57}{\frac{1.3468}{\sqrt{8}}}[/tex]

[tex]t = 2[/tex]

The p-value of the test is found using a right-tailed test, as we are testing if the mean is greater than a value, with t = 2 and 8 - 1 = 7 df.

  • Using a t-distribution calculator, this p-value is of 0.0428.

Since the p-value of the test is 0.0428 < 0.05, the sample provides convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price.

A similar problem is given at https://brainly.com/question/13873630

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