In: Statistics and Probability
1. Your sister, a consumer food advocate, is concerned about the mean fat content of the burgers you typically eat for lunch. She purchases 12 burgers from the restaurant and submits it to an independent laboratory for analysis. The percentage of fat in each burger is given by the following data:
21 18 19 16 18 24 22 19 24 14 18 15 The owner of the restaurant claims that the mean fat content of its burgers is no more than 20%. Assume that the percentage fat in a burger is normally distributed with a standard deviation of 3. Test whether there is evidence for the manufacturer’s claim. Let α = 0.05
a. Write down the type of test you will conduct.
b. Write down the null and alternative hypotheses.
c. Construct the test statistic.
d. Conduct the test.
e. What do you conclude?
2. Redo the previous question assuming that � is unknown.
a. Write down the type of test you will conduct.
b. Write down the null and alternative hypotheses.
c. Construct the test statistic.
d. Conduct the test.
e. What do you conclude?
Mean = (21+18+19+16+18+24+22+19+24+14+18+15)/12 = 228/12
Mean = 19
Answer 1a)
One sample z Test has been used to test the claim because population standard deviation is known.
Answer 1b)
This corresponds to a left-tailed test.
Answer 1c)
Answer 1d)
Rejection region:
Decision about the null hypothesis
Answer 1e)
Conclusion
At 0.05 significance level, there is not enough evidence to claim that the population mean μ is less than 20. In other words, at 0.05 significance level, there is not enough evidence to support owner's claim that the mean fat content of its burgers is no more than 20%
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