Question

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

      Ho:μ=75.5Ho:μ=75.5
      H1:μ>75.5H1:μ>75.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=120n=120 with a mean of M=78.4M=78.4 and a standard deviation of SD=7.9SD=7.9.

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 = 75.5
Alternative Hypothesis, Ha: μ > 75.5

Rejection Region
This is right tailed test, for α = 0.02 and df = 119
Critical value of t is 2.077.
Hence reject H0 if t > 2.077

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (78.4 - 75.5)/(7.9/sqrt(120))
t = 4.021

P-value Approach
P-value = 0.0001
As P-value < 0.02, reject the null hypothesis.

T distribution (invT for critical value)