Answer to Question #138867 in Statistics and Probability for ike

Question

The average expenditure per student, based on daily average attendance, for a certain school year was Php 496,176.00, with a population standard deviation of Php 74,880.00.

A survey for the next school year of 150 randomly selected students resulted in a sample average expenditure of Php 518,304.00. Do these results indicate that the average expenditure has decreased? Choose your own level of significance.

Answer 1

Null hypothesis $H_0: \mu =496176.$

Alternative hypothesis $H_a: \mu>496176.$

Level of significance: $\alpha =0.05.$

Test statistic: $z=\frac{\bar x-mu}{\frac{s}{\sqrt{n}}}=\frac{518304-496176}{\frac{74880}{\sqrt{150}}}=3.62.$

P-value: $p=P(Z>3.62)=0.0001.$

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

There is a sufficient evidence that the average expenditure has increased.