Answer to Question #188226 in Statistics and Probability for Ian

Question

It is estimated that senior high school students in a certain school spend an average amount of P400 monthly for sending text messages and making calls. A group of grade 11 students believe that the average monthly expenses in cellular phone load is less than P400. To verify their claim, the group randomly selected 20 students from grade 11 and 12 and obtained necessary information. The group found out that the sample mean is P356 with a standard deviation of P100. At 0.01 level of significance, is there enough evidence to support the claim of the group of grade 11 students?

Answer 1

Let, $H_o: \mu_1=\mu_2$ i.e. There is enough evidence to support the claim.

and $H_a:\mu\neq\mu_2$ i.e. There is not enought evidence to support the claim.

$x=400,\mu=356,\sigma=100,\alpha=0.01$

$Z_{\alpha}=Z_{0.01}=2.576$

Using z test statistics-

$z=\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}=\dfrac{(400-356)(\sqrt{20}}{100}=\dfrac{44\times \sqrt{20}}{100}=1.9677$

Conclusion: As the calculated value of $\alpha$ is less than the tabulated value at 0.01% significance level. Hence $H_o$ is accepted i.e. There is enough evidence to support the claim.