What's for Dinner Scenarios
You own the best nutritional consulting firm in America. You closely monitor trends and report your findings to local businesses and communities.
This Week, in particular, you are trying to learn information about America's eating habits by sampling Missouri residents. Your goal is to determine if America's consumption of cheese, beef, and beer is increasing.
There are three main roles in this scenario. Select a role and complete the task listed under the role.
Role #1 Cheese Analyst
In the U.S. Department of Agriculture's report in Food Consumption, Prices, and Expenditures in 2010, the average American consumed 33 lb's of cheese with a standard deviation of 6.9 lb's.
Your task is to determine if the average consumption in America last year is higher than in 2010. You took a random sample in Missouri and got the following data (in pounds per year): 46, 29, 33, 38, 42, 40, 34, 33, 32, 36, 28, 47, 26, 42, 36, 32, 45, 24, 39, 28, 33, 44, 33, 26, 37, 27, 31, 36, 37, 37, 36, 22, 44, 36, 29.
Identify the null and alternative hypothesis.
Would this be a two-tailed, left-tail, or right-tail hypothesis test?
Using a z-test and at a 10% significance level, does the data suggest that Americans are consuming more cheese than they did in 2010?
If an error was made, what type would it be? Explain.
Present your analysis to the group and to the leader.
Include your calculations and results.
Role #2 Beef Analyst
According to the same report by the U.S. Department of Agriculture (see Cheese Analyst), the average American consumed 57.5 pounds of beef. Your task is to determine if the average consumption in America is higher than in 2010. You took a random sample in Missouri and got the following data (in pounds per year): 70, 58, 50, 47, 61, 72, 49, 0, 43, 42, 44, 49, 49, 71, 56, 65, 0, 55, 67, 54, 54, 53, 49, 30, 69,70, 60, 60, 55, 82, 49, 68, 62, 66, 68, 55, 0, 64, 13, 40.
a. Identify the null hypothesis and alternative hypothesis.
b. Plot the histogram of and box and whisker plot of the sample data with and without outliers. Describe the plots.
c. Decide at a 5% significance level whether Americans are consuming more beef than they did in 2010 using the one mean t-test. Then repeat your hypothesis test after removing the outliers. Compare your results.
d. Assuming that the outliers are not recording errors, would it be advisable to remove the outliers? Explain.
e. Include your calculations and results.
Role #3 Beer Analyst
According to a report by the Kirin Beer University, the average American consumed 20.2 gallons of beer in 2011. Your task is to determine if the average consumption in America is higher than in 2011. You took a random sample in Missouri and got the following data (open the Chapter 9 review problems, number 41 to get the sample data).
a. Identify the null hypothesis and alternative hypothesis.
b. Plot the histogram of and box and whisker plot of the sample with and without outliers. Describe the plots. Can you see any outliers in your histogram?
c. Decide at a 1% significance level whether Americans are consuming more beer than they did in 2011. Then repeat your hypothesis test after removing the outliers. Compare your results.
d. Assuming that the outliers are not recording errors, would it be advisable to remove the outliers? Explain.
e. Include your calculations and results.