Question

The manufacturer of a well-known paint brand has developed a new product with properties that the manufacturer believes, surpasses the quality of its major competitor. In particular, they believe the new paint will provide superior coverage in a single coat. Before the manufacturer advertises that their paint coverage is superior to the competitor, the research and development (R and D) team for the company wants to test to determine the accuracy of the coverage claimed by the competing paint company. The competing company advertises that their paint will cover an average of 400 square feet per gallon. R and D randomly samples 10 gallon cans of the competitor paint and applies the paint in a controlled setting. The sample results for the 10 cans provided an average of 383 square feet coverage with a standard deviation of 20 square feet. Answer the following questions.......

A) Perform the appropriate hypothesis test to determine if the average coverage differs from the advertised 400 square feet.  Use alpha = .05. Make sure you include all required steps for the hypothesis test. Show work........ B) Compute a 95% confidence interval estimate for the mean coverage.......... C) Briefly explain how the confidence interval estimate supports the results of your hypothesis test.  

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Answer 1

a)

H0: the average coverage no differs from the advertised 400 square feet
H1: the average coverage differs from the advertised 400 square feet
Let the los be alpha = 5%

Test statistic
Z = (Xbar - Mu ) / (SD/sqrt(n))
= (383 - 400) / (20/sqrt(10))
= -2.6879
|Z| = 2.6879

Z critical value = +/- 1.96
Here |Z| value is not lies between Z critical values
So we reject H0

Thus we conclude that the average coverage differs from the advertised 400 square feet

b)

The 95% confidence interval of the population mean (A) is xt25%F-383 1.96-2. -(370.6039,395.3961)

c) The 95% chance that the poplation mean would be lies between (370.6039, 395.3961)