Question

A random sample of 91 fields of barley has a mean yield of 41.2 bushels per acre and standard deviation of 4.64 bushels per acre. Determine the 95% confidence interval for the true mean yield. Assume the population is normally distributed. Step 2 of 2 : Construct the 95% confidence interval. Round your answer to one decimal place.

Answer 1

solution

Given that,

= 41.2

= 4.64

n = 91

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96* (4.64 / 91)

= 0.95

=1 (rounded)

At 95% confidence interval mean is,

- E < < + E

41.2-1< < 41.2+1

40.2< < 42.2