Question

You wish to test the following claim (H1H1) at a significance level of α=0.005α=0.005.

      Ho:μ=57.7Ho:μ=57.7
      H1:μ≠57.7H1:μ≠57.7

You believe the population is normally distributed and you know the standard deviation is σ=12.4σ=12.4. You obtain a sample mean of M=53M=53 for a sample of size n=67n=67.

When finding the critical value and test statistic, which distribution would we be using?

• Normal distribution (invNorm for critical value)
• T distribution (invT for critical value)
• χ2χ2 distribution (invχχ for critical value)
• F distribution (invF for critical value)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 57.7
Alternative Hypothesis, Ha: μ ≠ 57.7

Rejection Region
This is two tailed test, for α = 0.005
Critical value of z are -2.807 and 2.807.
Hence reject H0 if z < -2.807 or z > 2.807

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (53 - 57.7)/(12.4/sqrt(67))
z = -3.103

P-value Approach
P-value = 0.0019
As P-value < 0.005, reject the null hypothesis.

Normal distribution (invNorm for critical value)