Mean Confidence Level- Keep Getting Incorrect Answers

Question

Assume that a sample is used to estimate a population mean μ. Find the 95% confidence interval for a sample of size 36 with a mean of 19.3 and a standard deviation of 10.7. Enter your answer accurate to one decimal place.I am 95% confident that the mean μ is between _______ and ________.

I really need help seeing how to do this problem and figuring out how to get the correct answer. Every answer I put into the homework program is incorrect. In this class the homework is not graded, just tests. I am trying to master the homework though so I can do better on the next test.

Answer 1

CI = mean +/- t-critical * standard error

t-critical for 95% confidence and sample size 36 is found by looking up the t-value corresponding to 0.025 upper tail probability and degrees of freedom = 36-1=35, which is 2.03.

standard error = standard deviation/square root of sample size = 10.7/6 = 1.78

CI = 19.3 +/- 2.03 * 1.78 = (15.69,22.91)