Question

The SAT scores of 20 randomly selected high school students has a mean of =1,185 and a sample standard deviation s=168.0. Construct an 98% confidence interval for the true population mean and interpret this interval

Answer 1

Solution :

Given that,

= 1,185

s = 168.0

n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,19 = .2.093

Margin of error = E = t_/2,df * (s /n)

= 2.093 * (168.0 / 20 )

= 78.62

Margin of error = 78.62

The 90% confidence interval estimate of the population mean is,

- E < < + E

1,185 - 78.62< < 1,185+ 78.62

1106.38 < < 1263.62

(1106.38, 1263.62)