Question 1041531: A study of 35 bolts of carpet showed that their average length was 70.2 yards. The standard deviation of the population is 1.6 yards. Which of the following is the 95% confidence interval for the mean length per bolt of carpet?
A. 69.1 < μ < 71.3
B. 69.9 < μ < 70.5
C. 69.8 < μ < 70.6
D. 69.7 <μ < 70.7
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The standard error is t(0.975, df=34)s/sqrt (n)
=2.0322*1.6/sqrt(35)
=0.5496, or 0.55
(69.65,70.75), which I would round to (69.7,70.7)
I would say D
BUT, I am bothered by the sd of the population and not the sample. I think what the question wants you to do is to use a z-test because the sample is larger than 30 AND you know the population sd. I don't have evidence of normality, which is another assumption needed, but if I accept that, then I would use a z-test but fortunately getting the same answer.
This would make it a z-test where the SE is 1.96*1.6/sqrt(35)=0,53, slightly different from above.
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