## Question 523:

1## Answer:

No answer provided yet.We'll need to compute a confidence interval around the mean to solve this one. To compute the interval we use the following steps:

- Find the mean and standard deviation of the 6 data-points. They are a
**mean**of 80.45 and**standard deviation**of 4.976. - Now we need to build the standard error around the mean (SEM) which is made up of the standard deviation divided by the square root of the sample size = 4.976/SQRT(6) = 2.0315.
- Next we build the margin of error, which is the SEM times a critical value from the t-distribution. We are using the t, instead of normal (or z) distribution because the sample is small and we don't know the population standard deviation. To find the critical value for 90% of the area under the t-curve we can look this value up in a t-table or use the excel function =TINV(.10,5) where the first parameter is the 1-confidence level, called alpha, and the second parameter is the degrees of freedom, or the sample size minus1. This gets us a critical value of 2.015
- The
**margin of error**the SEM*t-critical value = 2.0315*2.015 = 4.093 - To build our interval we add and subtract the margin of error to the mean. This gets us 80.45-4.093 and 80.45+4.093 = 76.36 to 84.54.

So the 90% confidence interval is between 76.36 and 84.54 making the answer the first choice.