Question 1200658
sample size is 7.
sampole mean is 15.2.
sample standard deviation is .7
critical t-score at 6 degrees of freedom at 95% confidence interval is equal to plus or minus 2.446911839.
t-score formula is t = (x-m)/s
t is the t-score
x is the confidence limits of the true mean.
m is the sample mean
s is the standard error.
standard error = .7/sqrt(7) = .2645751311.
on the low side, you get:
minus 2.446911839 = (x-15.2)/.2645751322.
solve for x to get x = 2.446911839 * .2645751322 + 15.2 = 14.5
on the high side, you get:
2.446911839 = (x - 15.2)/.2645751322.
solve for x to get x = 2.446911839 * .2645751322 + 15.2 = 15.9
the 95% confidence interval is from 14.5 to 15.9.
the true population mean will be within those limits 95% of the time.