Answer to Question #350979 in Statistics and Probability for beklogan21

Question

according to a study conducted by the grade 12 student, php 175 is the average monthly expenses for cell phone loads of high school students in their province.aA statistics students claim that this amount has increased since January of this year .do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of php164 for cellphone loads ? using 5% level of significance , assume that a population standard deviation is 53

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu\le175$

$H_1:\mu>175$

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is $\alpha = 0.05,$ and the critical value for a right-tailed test is $z_c = 1.6449.$

The rejection region for this right-tailed test is $R = \{z>1.6449\}.$

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{164-175}{53/\sqrt{50}}=-1.4676$$

6. Since it is observed that $z=-1.4676<1.6449=z_c,$ it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value for right-tailed is $p=P(Z>-1.4676)=0.928894,$ and since $p=0.928894>0.05=\alpha,$ it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean $\mu$

is greater than 175, at the $\alpha = 0.05$ significance level.