Question

A researcher suspects that a particular colony of elephants has mutated and now has a longer lifespan. The previous reported lifespan for the species of elephants was 65 years. She randomly selects 12 elephants from the colony and finds that their average lifespan was 78 years with a standard deviation of 9 years. Determine if the colony of elephants has a longer than average lifespan using a 5% significance level.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 65
Alternative Hypothesis, Ha: μ > 65

Rejection Region
This is right tailed test, for α = 0.05 and df = 11
Critical value of t is 1.796.
Hence reject H0 if t > 1.796

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (78 - 65)/(9/sqrt(12))
t = 5.004

P-value Approach
P-value = 0.0002
As P-value < 0.05, reject the null hypothesis.