A bottled water distributor wants to estimate the amount of water contained in 1

Question

A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally, known water bottling company. The water bottling company's specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.986 gallon, complete parts (a) through (d). a. Construct = 99% confidence Interval estimate for the population mean amount of water included in a 1-gallon bottle. b. On the basis of these results, do you think that the distributor has a right to complain to the water bottling company? Why? Yes No. Because a 1-gallon bottle containing exactly 1-gallon of water lies within outside the 99% confidence interval. c. Must you assume that the population amount of water per bottle is normally distributed here? Explain. A. Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is small. B. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small in this case, the value of n is small C. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally, distributed D. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is large. d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)? How does this change your answer to part (b)? A 1-gallon bottle containing exactly 1-gallon of water lies within outside the 95% confidence interval. The distributor still has now has still does not have now does not have a right to complete to the

Explanation / Answer

Confidence Interval formula:

X bar (-/+) E

X bar = sample mean = 0.986

E = zc * ( sigma / sqrt (n))

Zc is 2.58 for 99% confidence and 1.96 for 95% confidence

sigma = 0.02

n = 50

Question a)

Answer: 0.97871 < µ < 0.99329

Question b)

No, because a 1-gallon bottles containing exactly 1-gallon of water likes outside the 99% confidence interval.

Question c)

Option C: Yes, since nothing is known about the distribution of the population , it must be assumed that the population is normally distributed.

Question d)

0.98046 < µ < 0.99154

A 1-gallon containing bottle exactly 1-gallon of water lies outside the 95% confidence interval. The distribution still has a right complain to bottling company.

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