The Meat Suppose that Americans consume an average of 2 pounds of ground beef pe

Question

The Meat

Suppose that Americans consume an average of 2 pounds of ground beef per month.

(a)Do you expect the distribution of this measure (ground beef consumption per capita per month) to be approximately normal? Why or why not?

(b)Suppose you want to take a sample of 100 people. Do you expect the distribution of the sample meanto be approximately normal? Why or why not?

(c)You take a random sample of 100 Berkeley students to find out if their monthly ground beef consumptionis any different than the nation at large. The mean among your sample is 2.45 pounds and the samplestandard deviation is 2 pounds. What is the 95% confidence interval for students?

Explanation / Answer

Part a

Yes, we expect the distribution of this measure to be approximately normal, because given statement explains the average consumption of ground beef for all Americans and we know that the distribution for entire population data for the variable under study is approximately normal.

Part b

In the given scenario, we expect the distribution of the sample mean would be approximately normal distribution, because we know that the sampling distribution of the sample means or any other statistic follows an approximate normal distribution. Sampling distribution is the distribution of the sample statistics. Note that, we are considering the n number of sample means and not a single sample mean.

Part c

We are given

n = 100

Xbar = 2.45

S = 2

C = 95%

df = n – 1 = 100 – 1 = 99

Critical t value = 1.9842

Confidence interval = Xbar -/+ t*S/sqrt(n)

Confidence interval = 2.45 -/+ 1.9842*2/sqrt(100)

Confidence interval = 2.45 -/+ 1.9842* 0.2

Confidence interval = 2.45 -/+ 0.3968

Lower limit = 2.45 - 0.3968 = 2.0532

Upper limit = 2.45 + 0.3968 = 2.8468

Confidence interval = (2.0532, 2.8468)

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