A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nation
Posted: Wed May 11, 2022 11:26 am
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 0.01 gallon. A random sample of 50 bottles is
selected, and the sample mean amount of water per 1-gallon bottle
is 0.997 gallon. Complete parts (a) through (d).
Part 1 a. Construct a 95% confidence interval estimate for the
population mean amount of water included in a 1-gallon bottle.
enter your response here≤μ≤enter your response here (Round to five
decimal places as needed.)
Part 2 b. On the basis of these results, do you think that the
distributor has a right to complain to the water bottling company?
Why? ▼ No, Yes, because a 1-gallon bottle containing exactly
1-gallon of water lies ▼ within outside the 95% confidence
interval.
Part 3 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. 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. Yes, since nothing is known about the distribution of the
population, it must be assumed that the population is normally
distributed.
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 0.01 gallon. A random sample of 50 bottles is
selected, and the sample mean amount of water per 1-gallon bottle
is 0.997 gallon. Complete parts (a) through (d).
Part 1 a. Construct a 95% confidence interval estimate for the
population mean amount of water included in a 1-gallon bottle.
enter your response here≤μ≤enter your response here (Round to five
decimal places as needed.)
Part 2 b. On the basis of these results, do you think that the
distributor has a right to complain to the water bottling company?
Why? ▼ No, Yes, because a 1-gallon bottle containing exactly
1-gallon of water lies ▼ within outside the 95% confidence
interval.
Part 3 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. 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. Yes, since nothing is known about the distribution of the
population, it must be assumed that the population is normally
distributed.