1, the sampling standard deviation of the sample mean is equal to the square root of population standard deviation, that is, the square root of 40, that is, 6.3246.

2.90% confidence Excel = sampling standard error of sample mean * t (0.1/2,64-1) = 6.3246 * tinv (0.1.63) =10.56 (.

Note that the T-distribution critical value of Excel refers to the bilateral critical value.

Because your sample size is relatively large (greater than 50, preferably greater than 100), some textbooks may use the critical value of the standard normal distribution to replace the critical value of the T distribution in the above formula, and the computer results at this time will have some deviations:

Allowable error at 90% confidence level = sampling standard error of sample mean * z (0.1/2) = 6.3246 * normsinv (1-0.1/2) =10.40.

Note that the standard normal distribution critical value in Excel refers to one-sided critical value, so the significance level must be divided by 2, so it can be converted into two-sided critical value.

3. The lower limit of 90% confidence interval when the sample mean is 200 yuan =200- allowable error = 200-10.56 =189.44.

Upper limit of 90% confidence interval when the sample mean is 200 yuan =200+ allowable error = 200+10.56 = 210.56.