## Question 505:

1

This is a small set of continuous data so we'll use the critcal value from the t-distribution to generate the 98% confidence interval.

1. The mean of this data is 15.36
2. The standard deviation is .2387
3. The sample size 8.
4. Next we calculate the standard error of the mean (SEM) , which is the standard deviation divided by the square root of the sample size =  .2387/SQRT(8)  = .084
5. Now we find that critical value from the t-distribution. We'll use t instead of z here because we do not know the population standard deviation and the sample is rather small. We can use the excel formula = TINV(.02, 7), where .02 is our alpha or 1 minus the confidence level (1-.98) and 7 represents the degrees of freedom or N-1. You should get 2.997
6. Next we find the margin of error, which is made up of the SEM times the t-critical value = .084*2.997 = .253
7. To compute the confidence interval we add and subtract this margin of error from the mean = 15.36 + .253 and 15.36-.253 = a 98% Confidence Interval between 15.11 and 15.62.

To interpret this we'd say that over time if we were to take many samples from this population we'd expect the true population mean to fall within this interval (15.11 and 15.62) 98 percent of the time.