Question

n=25, sample mean= $30, s=6

a) would you reject the hypothesis that mean is 32 with type 1 error set at .05?

b) interpret results based on Tukey's three-decision rule.

Answer 1

H0: µ = 32

H1: µ ≠ 32, µ > 32 or µ < 32

µ = 32 , population mean

n = 25 , no. of observeations

s = 6, sample standard deviation

x = 30, sample mean

df, degrees of freedom = n-1 = 25-1 = 24

Test statistic, t = (x-µ)/(s/(n^0.5)) = (30-32)/(6/(25^0.5)) = (-2/(6/5)) = -1.67

For two-tailed,

H0: µ = 32

H1: µ ≠ 32

α = 0.05

Tabulated t, t1-α/2,df = t0.75,19 = 2.064

Since calculated t < tabulated t, we do not reject H0 and conclude that µ = 32.

For one-tailed,

H0: µ = 32

H1: µ > 32 or µ < 32

α = 0.05

Tabulated t, tα,df = t0.05,19 = 2.064

Since calculated t < tabulated t, we do not reject H0 and conclude that µ = 32.