Question 1201399
sample mean is 9.5 hours.
sample standard devition is 1.7 hours.
sample size is 15.
t-score is indicated because the standard deviation is taken from the sample rather than the population.
since you are looking at the mean of a sample of several elements, you would use the standard error rather than the standard deviation.
standard error = standard deviation / sqrt(sample size) = 1.7 / sqrt(15) = .4389381126.
t-score formula is t = (x - m) / s
t is the t-score
x is the upper or lower limit of the 95% considence interval.
m is mean of the sample.
s is the standard error.
the 95% confidence interval t-tscore with 14 degrees of freedom is plus or minus 2.144786681.
for the upper limit of the confidence interval, the t-score formula becomes:
2.144786681 = (x - 9.5) / .4389381126 
solve for x to get:
x = 2.144786681 * .4389381126 + 9.5 = 10.44142862.
for the lower limit of the confidence interval, the t-score formula becomes:
-2.144786681 = (x - 9.5) / .4389381126 
solve for x to get:
x = -2.144786681 * .4389381126 + 9.5 = 8.558571382.
your 95% confidence interval is 8.558571382 to 10.44142862.
round to two decimal places to get:
your 95% confidence interval is 8.56 to 10.44.