Answer to Question #196803 in Statistics and Probability for Fatine

Question

A journalist claims that the mean salary of middle class citizens in Casablanca is 9,600 MAD. To see how this compares to his neighborhood, a student surveyed 28 randomly selected middle class people and found that their mean income is 8,850 MAD. If the standard deviation for Casablanca middle class citizens is 1,000 MAD, can the student conclude that there is a difference at α = 0.10?

Answer 1

$H_o$ : there is a difference between means of population and sample

$H_{\alpha}$ : there is no a difference between means of population and sample

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\frac{8850-9600}{1000/\sqrt{28}}=-3.97$

From table for z-value:

p-value=$2P(z<-3.97)=2\cdot0.00004=0.00008$

Since p-value<$\alpha$ , we can reject null hypothesis.

So, there is no a difference between means of population and sample.