Question

The following data represent a random sample of 9 marks (out of 10) on a statistics quiz. The marks are normally distributed with a standard deviation of 2. Estimate the population mean with 90% confidence.

7 9 7 5 4 8 3 10 9

Answer 1

Mean $\bar x=\frac{7+9+7+5+4+8+3+10+9}{9}=6.889.$

$90\%CI=(\bar x-z_{0.05}\frac{\sigma}{\sqrt{n}},\bar x+z_{0.05}\frac{\sigma}{\sqrt{n}})=$

$=(6.889-1.645\frac{2}{\sqrt{9}},6.889+1.645\frac{2}{\sqrt{9}})=$

$=(5.792,7.986).$