The manager of a paint supply store wants to estimate the actual amount of paint
ID: 3367057 • Letter: T
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. It is known from the manufacturer's specifications 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 0.995 gallon. a. Set up a 99% confidence interval estimate of the true population mean amount of paint included in a 1-gallon can. b. On the basis of your results, do you think that the man ager has a right to complain to the manufacturer? Why? c. Does the population amount of paint per can have to be normally distributed here? Explain. d. Explain why an observed value of 0.98 gallon for an individual can is not unusual, even though it is out- side the confidence interval you calculated.Explanation / Answer
Ans:
a)99% confidence interval for true mean
=0.995+/-2.58*(0.02/sqrt(50))
=0.995+/-0.007
=(0.988,1.002)
b)No,as 1 gallon is included within above CI limits.
c)No,as sample size is sufficiently large i.e. n>=30
d)
Perdiction interval is always wider than the confidence interval,as perdiction interval is for single value and confidence interval is for mean value.So,0.98 will not unusual value.
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