Question 1191082
n = 100
sm = 37.6
ssd = 24.5
se = 24.5/sqrt(100) = 2.45
since the mean and standard deviation are from the sample, use the t-distribution.
at 90% two-tailed confidence interval, the critical t-score, with 99 degrees of freedom, will be equal to plus or minus 1.660 rounded to 2 decimal places.
t-score formula is:
t = (x - m) / se.
when t = -1.660, the t-score formula becomes:
-1.660 = (x - 37.6) / 2.45.
solve for x to get:
x = -1.660 * 2.45 + 37.6 = 33.533.
when t = 1.660, the t-score formula becomes:
1.660 = (x - 37.6) / 2.45.
solve for x to get:
x = 1.660 * 2.45 + 37.6 = 41.667
at 90% confidence interval, the sample mean will be between 33.533 and 41.667.
if many samples of 100 elements each were selected from the population, it is estimated that approximately 90% of these samples will contain the true population mean within the confidence limits and 10% of these samples intervals will not contain the true population mean within the confidence limits.