Answer to Question #125329 in Statistics and Probability for Hagan

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

Solution:

The provided sample mean is $\bar X = 3.16$ and the sample standard deviation is s = 0.70 and the sample size is n = 900

1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:μ = 3.18

Ha:μ < 3.18

This corresponds to a left-tailed test, Here, the sample size is greater than 30. So, it is appropriate to use one sample Z-test.

The t-statistic is computed as follows:

$t = \frac{\bar X - \mu_0}{s/\sqrt{n}} = \frac{ 3.16 - 3.18}{ 0.70/\sqrt{ 900}} = -0.857$

Using the P-value approach: The p-value is p = 0.1957 and since p=0.1957≥0.025, it is concluded that the null hypothesis is not rejected.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is less than 3.18, at the 0.025 significance level.