Question

Twenty-five adult citizens of the U.S. were asked to estimate the average income of all U.S. households. The mean estimate was x = $48,000 and s = $11,000. (Note: the actual average household income at the time of the study was about $68,000.) Assume the 25 adults in the study can be considered an SRS from the population of all adult citizens of the U.S. A 95% confidence interval for the mean estimate of the average income of all U.S. households is which of the following?

A.) $43,459 to $52,541

B.) $43,688 to $52,312

C.) $44,236 to $51,764

Answer 1

n = 25   = 48,000 Sx=$11.000

The population SD is not given so we will use the t-dist assuming the data follows normal distribution.

(1- )% is the confidence interval for population mean

Where

Alpha =1 - 0.95 = 0.05

Therefore the C.V. =

=

= 2.064 .............found using t-dist tables

Substituting the vlaue

Where Margin of error = C.v. * SE

=

A.) $43,459 to $52,541