Question

A psychologist wants to estimate the mean of IQ scores. It is widely believed that IQ scores follow a normal distribution. Her random sample of 20 IQ scores has a mean of 97 and a standard deviation of 17.6 . Find the 95% confidence interval for the population mean based on this sample. State the Best point estimate, Margin of Error and Include the written statement.

please list all the work.

Answer 1

Solution :

Given that,

= 97

s =14.6

n =20

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

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,19 =2.093 ( using student t table)

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

=2.093 * (17.6 / 20)

E = 8.2370

The 95% confidence interval estimate of the population mean is,

- E < < + E

97 -8.2370 < < 97+ 8.2370

88.7630< < 105.2370

( 88.7630,05.2370 )

point estimate = = 97