Answer to Question #315755 in Statistics and Probability for jephtha

Question

seven students were on a diet in an attempt to lose weight with 2 losing weight while the rest gaining weight. is the diet an effective way to losing weight

Answer 1

Let p denote the proportion of people who lose weight with the diet. The null hypothesis is that the diet is not effective, i.e. the proportion is 0.5, the alternative is that the proportion is greater than 0.5.

 

We have the

sample proportion

$\hat{p}=\frac{2}{7}$

The P- value

$P\left( \hat{p}\geqslant \frac{2}{7} \right) =P\left( \sqrt{n}\frac{\hat{p}-p}{\sqrt{p\left( 1-p \right)}}\geqslant \sqrt{n}\frac{\frac{2}{7}-p}{\sqrt{p\left( 1-p \right)}} \right) =\\=P\left( Z\geqslant \sqrt{7}\frac{\frac{2}{7}-0.5}{\sqrt{0.5\left( 1-0.5 \right)}} \right) =\\=P\left( Z\geqslant -1.13389 \right) =1-\Phi \left( -1.13389 \right) =0.87158$

Since the P-value is greater than $\alpha =0.01$ the null hypothesis is not rejected. The diet is not effective.