The manager of a paint supply store wants to estimate the actual amount of paint

Question

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.969 gallon. Complete parts (a) through (d). Construct a 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can lessthanorequalto mu lessthanorequalto (Round to five decimal places as needed.) On the basis of these results, do you think the manager has a right to complain to the manufacturer? Why? ________ because a 1-gallon paint can containing exactly 1-gallon of paint lies ___________ the 95% confidence interval. Must you assume that the population amount of paint per can is normally distributed here? Explain. No, because the Central Limit Theorem almost always ensures that X^bar is normally distributed when n is large. In this case, the value of n is large. Yes, because the Central Limit Theorem almost always ensures that X^bar is normally distributed when n is large. In this case, the value of n is small. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. No, because the Central Limit Theorem almost always ensures that X^bar is normally distributed when n is small. In this case, the value of n is small Construct a 90% confidence interval estimate. How does this change your answer to part (b)? lessthanorequalto mu lessthanorequalto (Round to five decimal places as needed.) How does this change your answer to part (b)? A 1-gallon paint can containing exactly 1-gallon of paint lies __________ the 90% confidence interval. The manager ___________ a right to complain to the manufacturer.

Explanation / Answer

here sample mean =0.969

std error =std deviation/(n)1/2 =0.0028

for 95% CI, z=1.96

hence confidence interval =sample mean -/+ z*std error =0.96346 ; 0.97454

b)Yes,,,,,outside of 95% confidence interval

c)option A is correct

d)for 90% CI, z=1.6449

Confidence interval =0.96435 ; 0.97365

paint lies outside the 90% the CI. The manager has a right...........

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