Answer:
Therefore the 95% confidence interval is (25,707.480 < E < 26,744.920)
Step-by-step explanation:
n = 77
mean u = 26,226.2 bushels per acre
standard deviation s = 2,322.32
let E = true mean
let A = test statistic
Find 95% Confidence Interval
so
let A = (u - E) * ([tex]\sqrt{n}[/tex] / s) be the test statistic
we want P( average_l < A < average_u ) = 95%
look for lower 2.5% and the upper 97.5% Because I think this is a 2-tail test
average_l = -1.96 which corresponds to the 2.5%
average_u = 1.96
P( -1.96 < A < 1.96) = 95%
P( -1.96 < (u - E) * ([tex]\sqrt{n}[/tex] / s) < 1.96) = 95%
Solve for the true mean E ok
E < u + 1.96* (s / [tex]\sqrt{n}[/tex])
from -1.96 < (u - E) * ([tex]\sqrt{n}[/tex] / s)
E < 26,226.2 + 1.96*( 2,322.32 / [tex]\sqrt{77}[/tex] )
E < 26,226.2 + 1.96*( 2,322.32 / [tex]\sqrt{77}[/tex] )
E < 26,226.2 + 518.7197348105429466
upper bound is 26,744.9197
or
u - 1.96* (s / [tex]\sqrt{n}[/tex]) < E
26,226.2 - 518.7197348105429466 < E
25,707.48026519 < E
lower bound is 25,707.48026519
Therefore the 95% confidence interval is (25,707.480 < E < 26,744.920)
