Question

A random sample of 100 recorded deaths in Kenya during the past year showed an average lifespan of 71.8 years with a standard deviation of 8.9 years. Does this seem to indicate that the average lifespan today is greater than 70 years at 0.05level of significance?

Answer 1

$H_0 : \mu = 70 \\ H_1 : \mu > 70$

Test statistic:

$t = \frac{\bar{x}- \mu}{s/ \sqrt{n}} \\ t = \frac{71.8-70}{8.9/ \sqrt{100}} = 2.02 \\ df= n-1=100-1=99 \\ α = 0.05$

$t_{crit}=1.98$ (table)

$t= 2.02 > t_{crit} = 1.98$

We can conclude that the null hypothesis is rejected.

The average lifespan today is greater than 70 years at 0.05 level of significance.