Question

Due to Covid 19, managers of mining companies are deciding to have fewer workers, the workers size in a company has decreased over the past months. According to Chamber of Mines report, the mean workers size was 3.18 in 2019. A researcher wanted to check if the current mean workers size is less than 3.18. A sample of 900 workers taken this year by this researcher produced a mean workers size of 3.16 with a standard deviation of 0.70. Using the 0.025 significance level, can you conclude that the mean workers size has decrease since 2019?

Answer 1

$H_0: \mu\geq3.18\\ H_1:\mu <3.18\\ \alpha =0.025\implies Z_{0.025}=1.96,\\ Z=\frac{\bar x-\mu_0}{\frac{s}{\sqrt n}}\\ Z=\frac{3.16-3.18}{\frac{0.7}{\sqrt {900}}}=-0.857\\ \text{the rejection region} :\; Z<-1.96\\ \text{The decision is to accept}:\; H_0\\ \text {This means that you cannot conclude that }\\ \text{ the mean workers size has decreased since 2019 }\\$