Question

In a certain population,it is claimed that the mean number of years of education is 13.3,while the standard deviation is known to be 2.7 years.A random sample of 70 people is drawn from this population,and the sample mean is 13.02 years.If the level of significance is set  to a=0.05,is there enough evidence to show that the claim is incorrect?

Answer 1

Let $H_o$ : The mean number of years of education is 13.3 i.e. $\mu_o=\mu,$

$\mu=13.3, \sigma=2.7\\ n=70, \text{ sample mean } x=13.02$

So, $z=\dfrac{(x-\mu)\sqrt{n}}{\sigma}=\dfrac{(13.02-13.3)\sqrt{70}}{2.7}=\dfrac{-0.28\times \sqrt{70}}{2.7}=-0.8675$

So The value of p calculted from the table is 0.3843.

The result is not significant as p < .05.

i.e. $H_o$ is rejected, The mean number of years of education is not 13.3, i.e. $\mu_o\neq \mu.$