Question

An extensive data base of numerically based performance evaluations exists for Fed-Ex employees where 5.0 is outstanding and 4.0 is above average performance. At the Indianapolis division, managers are trying to decide training needs. The following data are obtained: n = 34, x̄ = 4.14 and s = 0.53. At alpha 0.05 test the claim that the population of performance evaluations has a mean equal to 4.0. Address each of the following questions:

Is this a left tailed, right tailed or two tailed test?

What is the Null and Alternative Hypothesis and where is the claim?

What is Alpha?

What is the Critical Value?

What is the test statistic value and what formula did you use?

What is your decision?

State the final conclusion that addresses the original claim

Answer 1

Two tailed test

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 4
Alternative Hypothesis, Ha: μ ≠ 4

cliam is μ = 4

alpha = 0.05

Rejection Region
This is two tailed test, for α = 0.05 and df = 33
Critical value of t are -2.035 and 2.035.
Hence reject H0 if t < -2.035 or t > 2.035

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (4.14 - 4)/(0.53/sqrt(34))
t = 1.54

P-value Approach
P-value = 0.1331

As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the population of performance evaluations has a mean equal to 4.0.