Question

Finding x and E: A 95% confidence interval for a population mean is given as 32.8 < μ < 42.8. Round your answers to 1 decimal place.

(a) Calculate the sample mean.
x =

(b) Calculate the margin of error.
E =

Answer 1

a)

Confidence interval can be written in terms of and E as ( - E , + E)

Comparing this interval with (32.8 , 42.8) , we get

- E = 32.8 and + E = 42.8

Adding these two equation

2 = 32.8 + 42.8

= 37.8

b)

put value of in equation + E = 42.8 and solve for E

37.8 + E = 42.8

E = 5