Question

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001.

      Ho:μ=65.4Ho:μ=65.4
      H1:μ<65.4H1:μ<65.4

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=414n=414 with a mean of M=64M=64 and a standard deviation of SD=16.2SD=16.2.

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 = 65.4
Alternative Hypothesis, Ha: μ < 65.4

Rejection Region
This is left tailed test, for α = 0.001 and df = 413
Critical value of t is -3.11.
Hence reject H0 if t < -3.11

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (64 - 65.4)/(16.2/sqrt(414))
t = -1.7584

P-value Approach
P-value = 0.0397
As P-value >= 0.001, fail to reject null hypothesis.

T distribution (invT for critical value)