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C O 32% D Wed Feb 1 8:05 PM vamoi948 a EE Chrome File Edit View History Bookmarks People Window Help HW 2 Confidence Intervals Ch 8-Vincent Amoia Secure https:// Print 3. 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 deviation of the amount of paint is equal to 0.01 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.985 gallon. Complete parts (a) through (d). a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can. s H s (Round to five decimal places as needed.) b. On the basis of these results, do you think the manager has a right to complain to the manufacturer? Why? 1) because a 1-gallon paint can containing exactly 1-gallon of paint lies (2) the 99% confidence interval. c. Must you assume that the population amount of paint per can is normally distributed here? Explain. O A. 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 O B. Yes, because the Central Limit Theorem almost always ensures that Xis normally distributed when n is large. In this case, the value of n is small O C. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. O D. 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. d. Construct a 90% confidence interval estimate. How does this change your answer to part (b)? s H s (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 (3) the 90% confidence interval. The manager (4) a right to complain to the manufacturer. (1) O No. (2) O outside (3 O within O still has O within O outside O Yes, O now does not have O now has O still does not haveExplanation / Answer
3. population standard deviation is sigma=0.01
sample mean=Xbar=0.985
sample size=50
a) for 99% confidence interval alpha=0.01
hence the 99% confidence interval for population mean is
[Xbar-sigma*taoalpha/2/sqrt(n),Xbar+sigma*taoalpha/2/sqrt(n)]
where taoalpha/2 is the upper alpha/2 point of a N(0,1) distribution
now tao0.005=2.575829
hence the confidence interval is
[0.985-0.01*2.575829/sqrt(50),0.985+0.01*2.575829/sqrt(50)]=[0.981356,0.98864] [answer]
b) yes.because a one gallon paint can containing exactly 1 gallon of paint lies outside the 99% confidence interval
c) here sample size=n=50 which is quite large. so we dont need to assume anything about the distribution of population. central limit theorem will do the work
hence correct alternative is
A. No,because the central limit theorem almost always ensures that Xbar is normally distributed when n is large. in this case,the value of n is large.
d) for 90% confidence interval alpha=0.1
so taoalpha/2=tao0.05=1.644854
hence 90% confidence interval is
[0.985-0.01*1.644854/sqrt(50),0.985+0.01*1.644854/sqrt(50)]
[0.98267,0.98733] [answer]
A 1 gallon paint can containing exactly one gallon of paint lies outside the 90% confidence interval.the manager still has a right to complain to the manufacturer
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