Answer to Question #317811 in Statistics and Probability for gcogco

Question

Statistics students believe that the mean score on the first statistics test is 65. A

statistics instructor thinks the mean score is higher than 65. He samples ten statistics

students and obtains the scores 65 65 70 67 66 63 63 68 72 71. The data are assumed

to be from a normal distribution.

Construct a 90% confidence interval for the mean scores

Answer 1

$\mu=(65+65+70+67+66+63+63+68+72+71)/10=67$

$\sigma=\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{4+4+9+0+1+16+16+1+25+16}{9}}=3.2$

$CI=\mu \plusmn Z\frac{\sigma}{\sqrt{n}}=67 \plusmn 1.645 \frac{3.2}{\sqrt{10}}=67 \plusmn 1.66$