Question 1012650: use a normal distribution
or a t-distribution to construct a 95% confidence interval for the population
mean. Justify your decision. If neither distribution can be used, explain why.
In a random sample of 70 bolts, the mean length was
1.25 inches and the standard deviation was 0.05 inch
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! One key assumption is not known and that is whether the population is normally distributed. If you can assume that, then you would use a t-distribution, because you are estimating the sd using the sample sd. If you don't know whether the population is normally distributed, a sample of 70 may be sufficient, but if the population were extremely skewed, even 70 might be insufficient. Most people would probably invoke the Central Limit Theorem and say that 70 would be sufficient.
Continuing, given the population is such that a sample of 70 may be considered adequate,
t(0.975)=2.219
the interval is 2.219*0.05/sqrt (70)=0.0133
(1.2367,1.2633), or (1.24,1.26)
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