## Question 374:

1

1. We need to work backwards from the 95% confidence interval which has been provided. If we assume the interval to be symetrical, then the mean should be in the center. Since the margin of error is added to the mean, 1/2 the range of the confidence interval is the margin of error =  (9.64-7.82)/2 = .91. The mean would likely be .691.
2. The margin of Error is made up of the Standard Error of the Mean times a critical value from the t or z-distribution.
3. We know the sample size is small (14) and can quickly find the critical value from the t-distribution using Excel. Type =TINV(.05,13), where the parameters are 1-confidence level and the degrees of freedom or 1 less than the sample size. You should get 2.16. If we used the z or normal critical value we'd be using 1.96.
4. Dividing out the 2.16 from the Margin of Error of .91 gets us a Standard Error of the Mean of around .91/2.16= .42.
5. The Standard Error of the Mean is made up of the standard deviation divided by the square root of the sample size. We just need to setup an equation and solve for the unknown.
1. s/sqrt(14) = .42
2. s/3.714 = .42
3. s = 1.57

So the standard deviation given this confidence interval is probably really close to 1.57.