Finding the confidence interval for the true mean weight?

10 rabbits have an average weight of 9.6 ounces and the sample standard deviation is 0.30. What is the 95% confidence interval of the true mean weight?Finding the confidence interval for the true mean weight?
in this problem, u are given the following information





n= 10


x bar = 9.6


sigma = .3


95% confidence level





for a 95% confidence level, the value of z* is 1.96 so we know that





z*= 1.96





now u know that the formula for a confidence interval is





[x bar - z*(sigma/鈭歯), x bar + z*(sigma/鈭歯)]





so we just plug in those values





[9.6 - 1.96(.3/鈭?0), 9.6 + 1.96(.3/鈭?0)]





[9.6 - .1859, 9.6 + .1859]





[9.414, 9.786]





there is our confidence interval [9.414, 9.786]. a correct interpretation of this confidence interval is: we are 95% confident that the true mean weight of rabbits is between 9.414 oz and 9.786.Finding the confidence interval for the true mean weight?
If you use the normal distribution :





9.6 - 1.96 * 0.30 to 9.6 + 1.96 * 0.30





Or 9,012 to 10,188





For the 99 % confidence level you take 2.58 instead of 1.96





Since you tested only 10 rabbits you have to use the Student distribution. For a small sample the normal distribution is too optimistic.


Nine degrees of freedom will give you 2.26 instead of 1.96.


For 99 % this would be 3,25.