A research team did a survey on male smokers over 20 in Ontario to figure out the age when they started to smoke. Knowing that the starting age is normally distributed, a statistical test was run to test whether the average starting age is 15. 1000 male smokers were randomly selected and interviewed. The result shows that the sample standard deviation of the 1000 smokers is 5.144 and their average age of beginning to smoke is 16.
1.

Determine the null hypothesis:


Null Hypothesis: ${\mathrm{\mu}}_{0}=15$ (the actual mean)

2.

Substitute the information into the formula:


$t=\frac{\left(1615\right)}{\left(\frac{5.144}{\sqrt{1000}}\right)}=6.1475$


$p\mathrm{value}=\mathrm{Probability}\left(\leftT\right>6.1475\right)=\mathrm{Probability}\left(T<6.1475\right)+\mathrm{Probability}\left(T>6.1475\right)=p=1.136158\cdot {10}^{9}$, $T\u02dc\mathrm{StudentT}\left(999\right)$


This statistical test provides evidence that the null hypothesis is false, so we reject the null hypothesis.
