Answer to Question #213769 in Statistics and Probability for payat

Question

Example 3.3.1. San Miguel Corporation gives a monthly benefit to their employees during the COVID19 pandemic. They claimed that the average monthly benefit of their employees is at least Php 5

,

000.00

. A random samp\)35

employees were taken as samples to verify the said claim and found that their average monthly benefit is Php 6

,

000.00

 with a standard deviation of Php 600.00

. Is the company's claim correct at 0.05

 level of significance? Assume that the population is approximately normally distributed.

Answer 1

$H_0:\mu=5,000$

$H_a:\mu>5,000$

$n=35$

$\bar X=6,000$

$s=600$

$\alpha=0.05$

Population standard deviation is unknown, thus, t-score is used.

$t=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}$

$=\frac{6,000-5,000}{\frac{600}{\sqrt{35}}}$

$=9.86$

$CV=T_{0.05,34}=1.69$ Right tailed.

Since the test statistic 9.86 is greater than the critical value 1.69, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that San Miguel Corporation's average monthly benefit of their employees is at least Php 5,000.00