Question

HYPOTHESIS TESTING FOR THE MEAN (small sample) Question 04.

One recent study suggests that nation-wide average age at death from COVID-19 is 57 year. A county administrator wants to know if deaths from COVID-19 follows the same trend in her county as observed in rest of the world. Level of significance at 5%. Data was collected for 9 deaths recorded in the county so far and calculated following summary statistics: Average age = 63 years, sample standard deviation = 11 years. Test of average age in the county is different than the rest of the nation.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 57
Alternative Hypothesis, Ha: μ ≠ 57

Rejection Region
This is two tailed test, for α = 0.05 and df = 8
Critical value of t are -2.306 and 2.306.
Hence reject H0 if t < -2.306 or t > 2.306

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (63 - 57)/(11/sqrt(9))
t = 1.636

P-value Approach
P-value = 0.1405
As P-value >= 0.05, fail to reject null hypothesis.

Average age is not different than nation