Question

To construct a confidence interval for the difference between two population means mu 1 minus mu 2​, use the formula shown below when both population standard deviations are​ known, and either both populations are normally distributed or both n 1 greater than or equals 30 and n 2 greater than or equals 30. ​Also, the samples must be randomly selected and independent. left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus z Subscript c Baseline StartRoot StartFraction sigma Subscript 1 Superscript 2 Over n 1 EndFraction plus StartFraction sigma Subscript 2 Superscript 2 Over n 2 EndFraction EndRoot less thanmu 1 minus mu 2less thanleft parenthesis x overbar 1 minus x overbar 2 right parenthesis plus z Subscript c Baseline StartRoot StartFraction sigma Subscript 1 Superscript 2 Over n 1 EndFraction plus StartFraction sigma Subscript 2 Superscript 2 Over n 2 EndFraction EndRoot The descriptive statistics for the annual salaries from a random sample of microbiologists from two regions are shown below. Construct a​ 95% confidence interval for the difference between the mean annual salaries. x overbar 1equals​$108 comma 510​, n 1equals38​, and sigma 1equals​$9170​; x overbar 2equals​$85 comma 460​, n 2equals42​, and sigma 2equals​$9165 Complete the​ 95% confidence interval for mu 1 minus mu 2 below. ​$ nothingless thanmu 1 minus mu 2less than​$ nothing

Answer 1

for 95 % CI value of z=			1.96
margin of error E=z*std error =			4022.847
lower bound=(x1-x2)-E =			19027.15
Upper bound=(x1-x2)+E =			27072.85

from above 95% confidence interval for population mean =(19027.15 , 27072.85)