When setting up Confidence Interval to estimate the population mean, given sampl

Question

When setting up Confidence Interval to estimate the population mean, given sample mean and sample size n, if sample standard deviation s is given, you should use (fill in the blank by z or t) distribution to obtain the critical value; if population standard deviation sigma is given, you should use (z or t) distribution to obtain critical value. The inspection division of the Chattanooga CoCa-Cola Bottling Company is interested in estimating the actual amount of soft drink that is placed in 2-liter bottles. The bottling plant has informed the inspection division that the standard deviation for 2-liter bottles is 0.05 liter based on history data of many years (analogue to population standard deviation sigma). A random sample of 100 2-liter bottles obtained from the plant indicates a sample mean of 1.98 liters. Set up a 95% confidence interval estimate of the true population mean amount of soft drink in each bottle. You use (fill in the blank by z or t) distribution to obtain the critical value. The absolute critical value = The lower limit of the Cl = , the upper limit of the Cl =

Explanation / Answer

Question 13
(A) when population std. dev. is unknown and we have sample std. dev. t -distribution should be used to calculated the critical value.

(B)When population std. dev. is known z-distribution should be used to obtain critical value.

Question 14
mean = 2
std. dev. = 0.05
n = 100
sample mean = 1.98

(1) As population std. dev. is known, we should use z-distribution to obtain the critical value.

(2) The absolute critical value = 1.96

(3)
lower limit = 1.98 - 1.96*(0.05/sqrt(100)) = 1.9702
upper limit = 1.98 + 1.96*(0.05/sqrt(100)) = 1.9898

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