Question

Construct a 95​% confidence interval to estimate the population mean using the data below. x overbarequals37 sigmaequals10 nequals44 With 95​% ​confidence, when nequals44 the population mean is between a lower limit of 52.82 and an upper limit of 58.21. ​(Round to two decimal places as​ needed.)

Answer 1

With 95% confidence when n equals 44, the population mean is between a lower limit of 33.96 and an upper limit of 40.04

Explanation:

Confidence Interval = mean + or - Error margin (E)

mean = 37

sd = 10

n = 44

degree of freedom = n - 1 = 44 - 1 = 43

t-value corresponding to 43 degrees of freedom and 95% confidence level is 2.0165

E = t × sd/√n = 2.0165×10/√44 = 3.04

Lower limit = mean - E = 37 - 3.04 = 33.96

Upper limit = mean + E = 37 + 3.04 = 40.04

95% confidence interval is between 33.96 and 40.04