Question 1162064: 1)Suppose that I construct a confidence interval for the mean test grade on exam 1 using Statcrunch and get Upper Limit, 68.9 and a lower limit 76.3. State the conclusion for the confidence interval
2).What happens to the confidence interval as we increase the sample size? Explain your reasoning (explanations without reasoning will not be given credit.)
3)When should we use the t-distribution instead of the z-distribution?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! As you increase the sample size, the confidence interval will get smaller. This makes sense, because the larger the sample size, the more information you have about the population, essentially. Mathematically, the interval is inversely proportional to the sqrt of the sample size. The larger the sample, the more likely extreme values, which would widen the confidence interval, are cancelled out if you will by extreme values on the opposite side.
You use the z-distribution when you have the population sd sigma.
You use the t-distribution when the estimate of variance (and sd, which is sqrt of V) is taken from the sample sd itself.
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