Final answer:
To investigate if there is a difference between the mean wages of two companies, a Z-test is used to compare two independent sample means. The null hypothesis states that there is no difference between the two means. The decision to reject or not reject this hypothesis is made by comparing the test statistic to a critical value at the specified significance level.
Step-by-step explanation:
To determine if there is a significant difference between the mean hourly wages paid by two companies, we can perform a hypothesis test for two independent sample means. When the population standard deviations are known, we use a Z-test.
The null hypothesis (H0) for this scenario is that there is no difference between the mean wages of the two companies, denoted as μ1 = μ2, where μ1 is the mean wage for company A and μ2 is the mean wage for company B.
The alternative hypothesis (Ha) could be that there is a difference, which is expressed as μ1 ≠ μ2. The test statistic is calculated based on the sample sizes, sample means, and known population standard deviations. We would then compare the test statistic to a critical value from the Z-distribution at the 5% level of significance to decide whether to reject or not reject the null hypothesis.