Suppose a random sample of 60 bottles of \"CoughGone\" cough syrup was collected

Question

Suppose a random sample of 60 bottles of "CoughGone" cough syrup was collected and the alcohol content (in wt. percent) of each bottle measured. A 90 % confidence interval for bottle true mean alcohol content, , was then determined from these data to be (6.9, 9.4). It was assumed that the variance of the alcohol distribution was known. a.) What is the value of the sample mean, x?(Give answer to two places past decimal.) Submit Answer Tries 0/5 b.) what is the value of the population standard deviation, ? (Give decimal answer to two places past decimal.) Submit Answer Tries 0/5 c.) compared to the 90 % confidence interval above, a 85% confidence interval computed from the same data would be: a - wider b - narrower c same width d can't tell Submit Answer Tries 0/1 d.) which of the following statements best describes the meaning of a 90 % confidence interval for ? a-There is a 90 % chance that the value of is between 6.9 and 9.4 b-we can be highly confident that 90 % of all bottles of "CoughGone" cough syrup have an alcohol content between 6.9 and 9.4 wt. percent. If the process of selecting a random sample of size 60 and computing a 90 % confidence interval is repeated 100 times, we expect that 90 of the resulting intervals will include . Submit Answr Tries 0/1 e.) If the random sample size is increased from 60 to 90, what is the new width of the 90 % confidence interval? Assume the value of the population standard deviation, , remains unchanged. (Give decimal answer to two places past decimal.) Submit Answer Tries 0/5

Explanation / Answer

Solution:

a) sample mean = (6.9+9.4)/2 = 8.15

b) X + Z * s/sqrt(n) = 9.4
Z = 1.645
=> 1.645 * s/sqrt(60) = 9.4 -8.15
s/sqrt(60) = 1.25/1.645
s = 0.7598*sqrt(60)
s = 5.8853 = 5.89

c) option a - wider

d) option c - if the process of selecting a random sample of size 60 and computing a 90% confidence interval is repeated 100 times,90 of resulting intervals will include mu

e) width = U - L = 2(1.645)*(5.8853/sqrt(60)) = 2.4997 = 2.50
  

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