Question

An aging sheep cat, Mimi, gets regular checkups. Let X be a random variable that represents the cat's resting heart rate. From past experience, the vet knows x has a normal distribution with $\sigma$ = 12. This particular cat breed is known to have an average heart rate of 115 beats per minute. From Mimi's last six checkups, her heart rate measured: 93, 109, 110, 89, 117. At $\alpha$ = 0.05, is Mimi's heart rate slowing?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 115
Alternative Hypothesis: μ < 115

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (103.6 - 115)/(12/sqrt(5))
z = -2.12

P-value Approach
P-value = 0.0170
As P-value < 0.05, reject the null hypothesis.