## Question 451:

1## Answer:

No answer provided yet.- Calculate the
**standard error of the mean**: standard deviation / square root of the sample size = 15/SQRT(35) =2.54 - Find the
**critical value from the t-distribution**for 34 degrees of freedom and a probability of .05 (since this is for a 95% confidence interval). You can use MS Excel and type =TINV(.05,34) and should get 2.03. - Calculate the
**margin of error:**which is the standard error of the mean times the t-value =2.54*2.03 = 5.15 - Generate the Lower and Upper bounds of the confidence interval by adding and subtracting the margin of error to the mean = 82 +5.15= 87.15 and 82 -5.15 = 76.8.
- So your 95% confidence interval around the mean is (76.8, 87.15).

Using the same method above, the only difference for a 99% confidence interval is to substitute the new critical value in step 2 with =TINV(.01,34) = 2.73. Which gives you a new margin of error of 6.9. You should get a 99% CI of between (75.1, 88.9).

You can see that the 99% Confidence Interval is wider since we're asking for a higher level of confidence. As the confidence level increases the width of our interval also increases.