Question 1182685: Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies.
Here are summary statistics for randomly selected weights of newborn girls: n = 187, x̄ = 28.1 hg, s = 6.1 hg. The confidence level is 95%.
Select the correct choice below and, if necessary, fill in the blank to complete your choice.
A. tα/2 = __
(Round to two decimal places as needed.)
B. zα/2 = __
(Round to two decimal places as needed.)
C. Neither the normal distribution nor the t distribution applies.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It is a relatively large sample size, and if one believes in the rule of 30 regardless, a z-test would be used. However, I prefer using a t-test since the sd used is from the sample. The difference is <1% with a sample size this large. While the population weight is skewed somewhat, it is not likely to such a degree that a random sample of 187 could not be construed to be normally distributed.
t(alpha/2)=1.97
z(alpha/2)=1.96
If you've not studied the rule of 30 for sample size, use t.
If you were taught the rule of 30 means you can use z, use it.
But notice the small difference between the two with this sample size.
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