Question

4.28 Working backwards, two-sided: You are given the following hypotheses:

H₀: μ = 30
H_a: μ ≠ 30

We know that the sample standard deviation is 10 and the sample size is 70. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied.

The sample mean should be at most ____ or at least ____ (please round each answer to two decimal places)

Answer 1

Solution:

We are given

P-value = 0.05

S = 10

n = 70

Test is two tailed.

µ = 30

df = n – 1 = 69

t = 1.99494539 or -1.99494539

(by using t-table)

t = (Xbar - µ)/[S/sqrt(n)]

t = (Xbar – 30)/[10/sqrt(70)]

1.99494539 = (Xbar – 30)/ 1.1952

Xbar – 30 = 1.99494539*1.1952

Xbar – 30 = 2.38435873

Xbar = 30 + 2.38435873

Xbar = 32.38435873

When t = -1.99494539

-1.99494539 = (Xbar – 30)/ 1.1952

Xbar – 30 = -2.38435873

Xbar = 30 - 2.38435873

Xbar = 27.61564127

The sample mean should be at most 32.38 or at least 27.62.