Question 1204280
mean is equal to 27.414285714286
standard deviatiion is equal to 17.019736442478
sample size is 7.
t-score 80% confidence interval with 6 degrees of freedom = plus or minus t = 1.439755738.


i rounded intermediate values to 6 decimal places.
that's more than enough detail for a final rounding of 2 or 3 decimal digits.


the rounded values used are:
mean = 27.414286
standard deviation = 17.019736
degrees of freedom = sample size of 7 minus 1 = 6
critical t-score = plus oe minus 1.439756


t-score formula used is t = (x - m) / s
t is the t-score
x is the raw score
m is the mean
s is the standard error


to solve for x, the formula bgecomes:
x = s * t + m


standard error = standard deviation / sqrt(sample size).
that is equal to 17.019736 / sqrt(7) = 6.432856


on the high side of the confidence interval, you get x = s * t + m becomes:
x = 6.432856 * 1.439756 + 27.414286 = 36.676029.


on the low side of the confidence interval, you get x = s * t + m becomes:
x = 6.432856 * -1.439756 + 27.414286 = 18.152543.


your solution is 80% confidence interval for the sample mean = (18.15,36.68).