Question

Assume that population mean is to be estimated from the sample described. Use the sample results to approximate the margin of error and​ 95% confidence interval. Sample​ size, n=64​; sample​ mean, x overbare=83.0 ​cm; sample standard​ deviation, s=4.0 cm.

The margin of error is ____ cm. ​(Round to one decimal place as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 83.0

sample standard deviation = s = 4.0

sample size = n = 64

Degrees of freedom = df = n - 1 = 64 - 1 = 63

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,63 = 1.998

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

= 1.998 * ( 4.0 / 64)

Margin of error = E = 1.0 cm.