## Question 504:

1

Since this sample size is relatively small (30) I recommend building your confidence interval using the t-statistic. Assuming the data is roughly normally distributed:

1. The mean and standard deviation are .852 and .146  respectively for the GPAs.
2. Calculate the standard error of the mean: standard deviation / square root of the sample size = .852/SQRT(30) = .0265
3. Find the critical value from the t-distribution for 29 degrees of freedom and a probability of .05 (since this is for a 95% confidence interval). You can use MS Excel and type =TINV(.05,29) and should get 2.045
4. Calculate the which is the standard error of the mean times the t-value =.0265*2.045= .054
5. Generate the Lower and Upper bounds of the confidence interval by adding and subtracting the margin of error to the mean = .852-.054 and .852+.054 = .797 and .907.
6. So your 95% confidence interval around the mean GPA of .852 is (.797, .907).

In other words, we'd expect on average, the true unknown population mean to fall within this range(.797, .907) if we took repeated samples from these students.