SOLUTION: a sample of the mathematics test scores of 35 fourth graders has a mean of 78. past studies show that the standard deviation of fourth grade mathematics test scores was 12. find th
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Question 877703: a sample of the mathematics test scores of 35 fourth graders has a mean of 78. past studies show that the standard deviation of fourth grade mathematics test scores was 12. find the 90% confidence interval estimate of the mean mathematics scores of all fourth graders. Answer by Theo(13342) (Show Source):
confidence interval is equal to sample mean plus or minus margin or error.
sample mean is equal to 78.
sample error = population standard deviation divided by square root of sample size which is equal to 12 / sqrt(35) which is equal to 2.028 rounded to 3 decimal places.
critical z factor for a 90% confidence interval would be equal to 1.645 rounded to 3 decimal places.
margin of error = standard error * critical z factor = 1.645 * 2.028 = 3.336 rounded to 3 decimal places.
your confidence interval becomes equal to 78 plus or minus 3.336.
the lower limit is equal to 78 - 3.336 which is equal to 74.664
the upper limit is equal to 78 + 3.336 which is equal to 81.336
your 90% confidence interval is from 74.664 to 81.336.
here's a picture of your 90% confidence interval with its associated z-scores.
