Question

Next TWO questions are related to the following: To build a 95% interval estimate for the average commuting distance to the campus by IUPUI students, in a random sample of n = 80 students, the sample average distance was x̅ = 12.8 miles with a sample standard deviation of s = 3.2 miles. 8 The standard error of the mean is, a 0.822 b 0.732 c 0.526 d 0.358 9 The margin of error for the 95% interval estimate is, a 0.86 b 0.71 c 0.64 d 0.52.

Answer 1

Solution :

Given that,

$\bar x$ = 12.8

s =3.2

n = Degrees of freedom = df = n - 1 = 80- 1 = 79

standard error (SE) = (s /$\sqrt$n) = (3.2/$\sqrt$80) =0.358

a ) At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

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

t_{$\alpha$ /2,df} = t_0.025,79 = 1.990

Margin of error = E = t_{$\alpha$/2,df} * SE

= 1.990 *0.358

E=0.71