Question

The following 94% C.I.for u was obtained from a sample of 27 observations (the population variance is known); (-2290.1232, 259.6632)

1) What is xbar?

2) What is sigma?

please explain in detail with step by step?

Answer 1

1) xbar = (Upper Limit + Lower limit)/2 = (259.6632 - 2290.1232)/2 = -1015.23

2) Margin of error = (Upper limit - Lower limit)/2 = (259.6632 - (-2290.1232))/2 = 1274.893

Since population variance is known, we will use z confidence interval in this case. From standard normal table:

P(z < -1.88) = 0.03

So,

P(z > 1.88) = 0.03

And

P(-1.88 < z < 1.88) = 1 - 2*0.03 = 0.94

By the formula for margin of error:

= 3523.691