Question

Note: Each bound should be rounded to three decimal places.

A random sample of n=100 observations produced a mean of x̅=28 with a standard deviation of s=6.

(a) Find a 90% confidence interval for ?
Lower-bound:  Upper-bound:

(b) Find a 99% confidence interval for ?
Lower-bound:  Upper-bound:

(c) Find a 95% confidence interval for ?
Lower-bound:  Upper-bound:

Answer 1

n=100, =28, s=6.

a)

formula for confidence inerval is

Where tc is the t critical value for c=90% with df=99

tc= 1.66

(28−0.996 < < 28+0.996)

= (27.004, 28.996)

Lower-bound: 27.004

Upper-bound: 28.996

b)

formula for confidence inerval is

Where tc is the t critical value for c=99% with df=99

tc= 2.626

(28−1.576 < < 28+1.576)

= (26.424 , 29.576)

Lower-bound:  26.424

Upper-bound: 29.576

c)

formula for confidence inerval is

Where tc is the t critical value for c=95% with df=99

tc= 1.984.

( 28−1.191 < < 28+1.191 )

= (26.809 , 29.191)

Lower-bound:  26.809

Upper-bound:  29.191