Answer to Question #188386 in Statistics and Probability for Shanley Encabo

Question

According to a study done last year, the average monthly expenses for mobile phone loads of senior high school students in Sta. Rosa was P350.00. A statistics student believes that this amount has increased since January of this year. Is there a reason to believe that this amount has really increased if a random sample of 60 students has an average monthly expenses for mobile phone loads of P380.00? Use a 0.05 level of significance. Assume that the population standard deviation is P77.00.

Answer 1

Let, Null hypothesis $H_0$ : $\mu>P350$

Alternative hypothesis $H_{\alpha}$ : $\mu\leq350$

Test statistic:

$z=\dfrac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{380-350}{77/\sqrt{60}}=3.02$

P-value:

$p=P(z>3.02)=1-0.9987=0.0013$

Since the P-value is less than 0.05, reject the null hypothesis.

So, we can conclude that monthly expenses for cell phone loads was not really increased since January of this year.