Question

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

      Ho:μ=58.5Ho:μ=58.5
      H1:μ>58.5H1:μ>58.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=12n=12 with a mean of M=80.4M=80.4 and a standard deviation of SD=18.5SD=18.5.

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 = 58.5
Alternative Hypothesis, Ha: μ > 58.5

Rejection Region
This is right tailed test, for α = 0.002 and df = 11
Critical value of t is 3.624.
Hence reject H0 if t > 3.624

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (80.4 - 58.5)/(18.5/sqrt(12))
t = 4.101

P-value Approach
P-value = 0.0009
As P-value < 0.002, reject the null hypothesis.

T distribution (invT for critical value)