<p>A line manager at a Coca Cola plant claims that one machine on average is dis

Question

<p>A line manager at a Coca Cola plant claims that one machine on average is dispensing significantly more than 12 ounces of Coke into cans. Given that the cans are labeled "12 oz.", they set up the hypotheses below (&#956; is the mean volume in ounces of the Coke in a sample of 36 different cans).</p>
<p>H_o:&#956; = 12 ounces</p>
<p>H₁:&#956; &gt; 12 ounces</p>
<p>a. If you were to perform a hypothesis test for the line manager, explain how you decide whether to get critical values from the standard normal distribution or the Student's t-distribution?</p>
<p>b. Is this a Right-Tailed Test, Left-Tailed Test, or a Two-Tailed Test?</p>
<p>c. Suppose the decision turns out to be "reject H_o", what conclusion can be drawn about the mean amount of soda dispensed by this machine into Coke cans labeled "12 oz."?</p>
<p>d. Suppose it is later discovered that the null hypothesis is TRUE, has a Type I or Type II error been made? How could this kind of error affect the Coca Cola Company?</p>

Explanation / Answer

a. I would use from the t distribution because I am going to be using s to estimate sigma for the population. Also the sample size is small. b. right tail (he believes more) c. the p value is significantly small, small enough for me to reject the null hypothesis. Data shows that one machine on average likely is dispensing more than 12 ounces of Coke into cans. d. If the null hypothesis is rejected when it is in fact true (and the patient is well), this is a Type I error. It means they fixed a machine for nothing. Probably not much... it's a billion dollar company.

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