The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. A random sample of 6 Ontario banks is selected and that the bad debt ratios (in percentages) for these banks are:
7 4 6 7 5 8
Compute and interpret a 95% confidence interval for the mean bad debt ratio. What needs to be true in order for this interval and interpretation to be valid?
I started off by finding the mean: (7+4+6+7+5+8)/6 = 6.167, but I am confused as to how to find the variance of 2.167.
I continued using the answer for the variance and did: 6.167 + 1.96*(1.4721/sqrt6) , 6.167 - 1.96*(1.4721/sqrt6), and I got the answer of [4.987, 7.347], but the answer says [4.62,7.71].
Any help as to how to find the variance and where I went wrong in my confidence interval is very appreciated! Thank you!