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A soft-drink manufacturer claims that its 12-ounce cans do not contain, on average, more than 30 calories.

A soft-drink manufacturer claims that its 12-ounce cans do not contain, on average, more than 30 calories.  A random sample of 16 cans of this soft drink, which were checked for calories, contained a mean of 31.8 calories with a standard deviation of 3 calories.  Assume that the number of calories in 12-ounce soda cans is normally distributed.
a) State the null and alternative hypotheses.
b) Select the distribution to use.  Explain briefly why you selected it.
c) Assuming that they wish to test the claim at alpha = 0.025, determine the rejection and non rejection regions based on your hypotheses in a).  State the critical value.
d) Calculate the value of the test statistic.
e) Does the sample information support that the manufacturer's claim is false?  Explain your conclusion in words.

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