Question

# The manager of a paint supply store wants to determine whether the mean amount of paint...

The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacture is actually 1 gallon. You know from the manufactures specification that the standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of painter per 1-gallon can is 0.995.

(a) Conduct a hypothesis test to determine whether or not there’s enough evidence to conclude that the mean paint amount is different than 1.0 gallon by doing the following:

i. List the null and alternate hypotheses

ii. Find the value of the test statistic. iii. List the decision rule. (Use α = 0.01.)

iv. Answer the following question in a complete sentence for your conclusion: Is there evidence that the mean amount is different from 1.0 gallon? Why or why not (refer to the decision rule here)?

(b) Compute the p-value and interpret its meaning.

(c) Construct a 99% confidence interval estimate of the population mean amount of paint.

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