Question

statistics question.

Question 14 0/2 View Policies Show Attempt History Current Attempt in Progress Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. A 95% confidence interval for a mean if the sample has n=40 with T=63 and 13 S = , and the standard error is SE = 2.06 Round your answers to three decimal places The 95% confidence interval is to

Answer 1

Solution :

Given that,

$\bar x$ = 63

s = 13

n = 40

Degrees of freedom = df = n - 1 = 40 - 1 = 39

At 95% confidence level the t is ,

$\alpha$  = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

t_{$\alpha$ /2,df} = t_0.025,39 = 2.021

Standard error = (s /$\sqrt$n)

= (13 / $\sqrt$ 40)

= 2.055

Standard error = 2.06

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.021 * (13 / $\sqrt$ 40)

= 4.163

Margin of error = 4.163

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

63 - 4.163< $\mu$ < 63 + 4.163

58.837 < $\mu$ < 67.163

(58.83, 67.163 )