Beef Consumption. According to Food Consumption, Prices, and Expenditures, published by the U.S. Department of Agriculture, the mean consumption of beef per person in 2011 was 57.5 lb. A sample of 40 people taken this year yielded the data, in pounds, on last year’s beef consumption given on the WeissStats site. Use the technology of your choice to do the following. a. Obtain a normal probability plot, a boxplot, a histogram, and a stem-and-leaf diagram of the data on beef consumptions. b. Decide, at the 5% significance level, whether last year’s mean beef consumption is less than the 2011 mean of 57.5 lb. Apply the onemean t-test. c. The sample data contain four potential outliers: 0, 0, 0, and 13. Remove those four observations, repeat the hypothesis test in part (b), and compare your result with that obtained in part (b). d. Assuming that the four potential outliers are not recording errors, comment on the advisability of removing them from the sample data before performing the hypothesis test. e. What action would you take regarding this hypothesis test?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Beef Consumption. According to Food Consumption, Prices, and Expenditures, published by the U.S. Department of Agriculture, the mean consumption of beef per person in 2011 was 57.5 lb. A sample of 40 people taken this year yielded the data, in pounds, on last year’s beef consumption given on the WeissStats site. Use the technology of your choice to do the following.
a. Obtain a normal probability plot, a boxplot, a histogram, and a stem-and-leaf diagram of the data on beef consumptions.
b. Decide, at the 5% significance level, whether last year’s mean beef consumption is less than the 2011 mean of 57.5 lb. Apply the onemean t-test.
c. The sample data contain four potential outliers: 0, 0, 0, and 13. Remove those four observations, repeat the hypothesis test in part (b), and compare your result with that obtained in part (b).
d. Assuming that the four potential outliers are not recording errors, comment on the advisability of removing them from the sample data before performing the hypothesis test.
e. What action would you take regarding this hypothesis test?
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