A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nation
Posted: Mon Jul 11, 2022 11:24 am
A bottled water distributor wants to estimate the amount ofwater contained in 1-gallon bottles purchased from a nationallyknown water bottling company. The water bottling company'sspecifications state that the standard deviation of the amount ofwater is equal to 0.03 gallon. A random sample of 50 bottles isselected, and the sample mean amount of water per 1-gallon bottleis 0.948 gallon. Complete parts (a) through (d).
Question content area bottom Part 1 a. Construct a 99%confidence interval estimate for the population mean amount ofwater included in a 1-gallon bottle. enter your responsehere≤μ≤enter your response here (Round to five decimal places asneeded.)
Part 2 b. On the basis of these results, do you think that thedistributor has a right to complain to the water bottling company?Why? ▼ No, Yes, because a 1-gallon bottle containing exactly1-gallon of water lies ▼ outside within the 99% confidenceinterval.
Part 3 c. Must you assume that the population amount of waterper bottle is normally distributed here? Explain. A. Yes, sincenothing is known about the distribution of the population, it mustbe assumed that the population is normally distributed. B. Yes,because the Central Limit Theorem almost always ensures that X isnormally distributed when n is large. In this case, the value of nis small. C. No, because the Central Limit Theorem almost alwaysensures that X is normally distributed when n is large. In thiscase, the value of n is large. D. No, because the Central LimitTheorem almost always ensures that X is normally distributed when nis small. In this case, the value of n is small.
Part 4 d. Construct a 90% confidence interval estimate. Howdoes this change your answer to part (b)? enter your responsehere≤μ≤enter your response here (Round to five decimals)
question number 2
In a studyof 426 nonprofits nationwide, 82 indicatedthat turnover has been the biggest employment challenge at theirorganization. Complete parts (a) through (c).
95%
enter your response here≤π≤enter your response here
(Type integers or decimals. Round to three decimal placesas needed.)
Interpret the interval constructed in part (a).
Choose the correct answer below.
A.With
5%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thesample is in this interval.
B.With
95%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thesample is in this interval.
C.With
95%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thepopulation is in this interval.
D.With
5%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thepopulation is in this interval.
Part 3
c.
±0.04
95%
confidence, how many nonprofits would you survey?
sample of
enter your response here
nonprofits should be surveyed. (Round up to thenearest integer.)
Question content area bottom Part 1 a. Construct a 99%confidence interval estimate for the population mean amount ofwater included in a 1-gallon bottle. enter your responsehere≤μ≤enter your response here (Round to five decimal places asneeded.)
Part 2 b. On the basis of these results, do you think that thedistributor has a right to complain to the water bottling company?Why? ▼ No, Yes, because a 1-gallon bottle containing exactly1-gallon of water lies ▼ outside within the 99% confidenceinterval.
Part 3 c. Must you assume that the population amount of waterper bottle is normally distributed here? Explain. A. Yes, sincenothing is known about the distribution of the population, it mustbe assumed that the population is normally distributed. B. Yes,because the Central Limit Theorem almost always ensures that X isnormally distributed when n is large. In this case, the value of nis small. C. No, because the Central Limit Theorem almost alwaysensures that X is normally distributed when n is large. In thiscase, the value of n is large. D. No, because the Central LimitTheorem almost always ensures that X is normally distributed when nis small. In this case, the value of n is small.
Part 4 d. Construct a 90% confidence interval estimate. Howdoes this change your answer to part (b)? enter your responsehere≤μ≤enter your response here (Round to five decimals)
question number 2
In a studyof 426 nonprofits nationwide, 82 indicatedthat turnover has been the biggest employment challenge at theirorganization. Complete parts (a) through (c).
95%
enter your response here≤π≤enter your response here
(Type integers or decimals. Round to three decimal placesas needed.)
Interpret the interval constructed in part (a).
Choose the correct answer below.
A.With
5%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thesample is in this interval.
B.With
95%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thesample is in this interval.
C.With
95%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thepopulation is in this interval.
D.With
5%
confidence, the proportion of nonprofits that indicate turnoveras the biggest employment challenge at their organization in thepopulation is in this interval.
Part 3
c.
±0.04
95%
confidence, how many nonprofits would you survey?
sample of
enter your response here
nonprofits should be surveyed. (Round up to thenearest integer.)