Question

The state test scores for 12 randomly selected high school seniors are shown on the right. Completo parts (a) through 1425 (c) below 697 720 Assume the population is normally distributed 628 1221 729 747 1446 980 837 546 946 (a) Find the sample mean (Round to one decimal place as needed.) (b) Find the sample standard deviation (Round to one decimal place as needed.) (c) Construct a 99% confidence interval for the population mean A 99% confidence interval for the population meanis . (Round to one decimal place as needed.) SE

Answer 1

a)  
T
=  
Σ. .. n
= 910.1667  $\approx$910.2

b) s =  $\sqrt{\frac{\sum x^{2}-n*\bar{x}^{2}}{n-1}}$ = 303.5526  $\approx$303.6

c) In general, (1-$\alpha$)% confidence interval for population mean is obtained as follows :
$(\bar{x}\mp t_{\alpha/2,n-1}*s*\frac{1}{\sqrt{n}})$
Here t ($\alpha$/2, n-1) = t (0.005, 11) = 3.4966

Thus, 99% confidence interval for population mean is :
$(910.1667-3.4966*303.5526*\frac{1}{\sqrt{12}},910.1667+3.4966*303.5526*\frac{1}{\sqrt{12}})$

$\Rightarrow$ ( 603.7663 , 1216.5671 )

$\Rightarrow$ ( 603.8 , 1216.6 )

Hope this answers your query!