Question

Twenty‑five adult citizens of the United States were asked to estimate the average income of all U.S. households. The mean estimate was ¯ x = $ 65 , 000 and s = $ 15 , 000 . (Note: The actual average household income at the time of the study was about $ 79 , 000 .) Assume the 25 adults in the study can be considered an SRS from the population of all adult citizens of the United States. Which of the statements would cause the most worry about the validity of a 95 % confidence interval for the mean estimate of the average income of all U.S. households based on the information?

a. $58,808 to $71,192 .
b. $62,808 to $72,192 .
c. $43,000 to $73,040 .
d. $30,808 to $85,192 .

Answer 1

a) 95 % confidence interval for the mean estimate of the average income of all U.S. households based on the information

(58,808 ,71,192)

Step-by-step explanation

Step-by-step explanation:-

Given data assume the 25 adults in the study can be considered an SRS from the population of all adult citizens of the United States.

Given sample size 'n' =25

The mean estimate x⁻ = $ 65 , 000

sample standard deviation 's' = $ 15 , 000

Degrees of freedom γ= n-1 =25-1=24

The tabulated value t = 2.0639 (check t- table blue mark) at 0.05 level of significance with 24 degrees of freedom.

Step(ii):-

95 % confidence interval for the mean

`(x^(-) - t_(\alpha ) (S)/(√(n) ) ,x^(-) +t_(\alpha ) (S)/(√(n) ) )`

`(65000- 2.0639 (15000)/(√(25) ) ,65000 +2.0639 (15000)/(√(25) ) )`

(65,000-6191.7 ,65,000+6191.7)

(58,808 ,71,192)

Conclusion:-

95 % confidence interval for the mean estimate of the average income of all U.S. households based on the information

(58,808 ,71,192)