Answer:
Insured persons:
Population sd = $4,391.4
Population variance = 19,284,393.96 square dollars
Uninsured persons:
Population sd = $10,123.5
Population variance = 102,485,252.3 square dollars
The cost interval for insured persons is less than that of uninsured persons.
Explanation:
Insured persons:
98% confidence interval is ($17,627, $25,462)
Lower limit = $17,627
Upper limit = $25,462
Margin of error (E) = (upper limit - lower limit) ÷ 2 = (25,462 - 17,627) ÷ 2 = 7,835 ÷ 2 = $3917.5
n = 10
degree of freedom = n-1 = 10-1 = 9
confidence level (C) = 98% = 0.98
significance level = 1 - C = 1 - 0.98 = 0.02 = 2%
critical value (t) corresponding to 9 degrees of freedom and 2% significance level is 2.821
Population sd = E×√n/t = 3917.5×√10/2.821 = $4391.4
Population variance = (population sd)^2 = ($4391.4)^2 = 19,284,393.96 square dollars
Uninsured persons:
98% confidence interval is ($40,640, $58,702)
Lower limit = $40,640
Upper limit = $58,702
Margin of error (E) = (58,702 - 40,640) ÷ 2 = 18,062/2 = $9,031
n = 10
degree of freedom = n-1 = 10-1 = 9
significance level = 2%
critical value (t) = 2.821
Population sd = E×√n/t = 9,031×√10/2.821 = $10,123.5
Population variance = ($10,123.5)^2 = 102,485,252.3 square dollars.
The cost interval for insured persons is less than than that of uninsured persons.
