Question

Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed.

A 90% confidence interval for a mean μ if the sample has n=100 with x¯=22.1 and s=5.6, and the standard error is SE=0.56.

Round your answers to three decimal places.

The 90% confidence interval is Enter your answer; The 90% confidence interval, value 1 to Enter your answer; The 90% confidence interval, value 2 .

Answer 1

Solution :

Given that,

= 22.1

s = 5.6

n = 100

Degrees of freedom = df = n - 1 = 100 - 1 = 99

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,99 = 1.660

The standard error = SE = (s /n)

= (5.6/ 100 )

= 0.56

The standard error = 0.56

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

= 1.660 * (5.6/ 100 )

= 0.930

Margin of error = 0.930

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

- E < < + E

22.1 - 0.930 < < 22.1+ 0.930

21.170 < < 23.03

(21.170, 23.03 )