SOLUTION: Could you please tell me if the following is correctly calculated: Construct a 90% confidence interval for a mean of a normal population, given a random sample of 12 values with a

Question 957689: Could you please tell me if the following is correctly calculated:
Construct a 90% confidence interval for a mean of a normal population, given a random sample of 12 values with a mean and standard deviation of 270 and 14.6, respectively.
I used t-interval and the answers were (262.43, 277.57)
Please let me know if I am calculating this properly - Thank you in advance.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean of the sample is 270
standard deviation of the sample is 14.6
number of items in the sample is 12.

you need to find the standard error.

se = sds / sqrt(n)

se is the standard error.
sds is the standard deviation of the sample.
n is the number of items in the sample.

formula becomes se = 14.6 / sqrt(12) = 4.2147 rounded to 4 decimal places.

you need to find the critical t-value.

for a 90% confidence interval, your two tailed alpha is 10%.

your degrees of freedom would be 12 - 1 = 11.

you would look up a critical t-value for two tailed alpha of .10 and 11 degrees of freedom.

that would get you a critical t-score of 1.796.

your margin of error would be mean plus or minus critical t-score times your standard error.

your margin of error becomes 270 plus or minus 1.796 * 4.2147 which becomes 270 plus or minus 7.57 rounded to 4 decimal places.

this would result in a confidence interval of between 262.43 and 277.57.

i believe you got it right.

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