SOLUTION: You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 10. Find the critical value th

Question 1119721: You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 10.
Find the critical value that corresponds to a confidence level of 99.5%.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size is 10.

standard error is standard deviation divided by square root of population size.

if you use z-scores, and it appears that you have to, since you don't know the mean or standard deviation of your population, your mean is 0 and your standard deviation is 1.

at 99.5% confidence level, 100% - 99.5% is your alpha.

that makes it equal to .5%.

divide that by 2 and you have half your alpha on the left end of the confidence interval and half on the right end.

that makes it 2.5% on each end.

2.5% is the same as .025 in decimal form.

look up a z-score to the left of .025 to get a z-score of -1.959963986 which can be rounded to -1.96.

since the normal distribution is symmetric about the mean, then your critical z-score is plus or minus 1.96.

that means .025 of the area under the normal distribution is to the left of -1.96 and .025 of the area under the normal distribution is to the right of 1.96.

that distribution would look like this.

inside the confidence interval:

$$$

outside the confidence interval:

$$$

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