Final answer:
In this scenario, a hypothesis test is performed to determine if the mean annual income of certified welders is different from $50,050. The results of the test indicate that there is not enough evidence to conclude that the welders earn either more or less than $50,050 annually.
Step-by-step explanation:
In this scenario, we are given a normal distribution of the mean annual incomes of certified welders with a mean of $50,050 and a population standard deviation of $2,000. We are also given a sample of 100 welders with a mean annual income of $50,250. To determine whether the welders earn more or less than $50,050 annually, we need to conduct a hypothesis test.
Null hypothesis (H0):
The mean annual income of the welders is equal to $50,050. (μ = $50,050)
Alternative hypothesis (Ha):
The mean annual income of the welders is not equal to $50,050. (μ ≠ $50,050)
Using a significance level of 0.05, we can perform a t-test to determine if we have enough evidence to reject the null hypothesis. We compare the sample mean ($50,250) to the population mean ($50,050) and calculate the t-value using the formula:
t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
In this case, the t-value is calculated as:
t = (50250 - 50050) / (2000 / sqrt(100)) = 1.0
Next, we compare the t-value to the critical t-value at a 0.05 significance level with 99 degrees of freedom. If the calculated t-value falls within the critical region, we can reject the null hypothesis and conclude that the welders earn either more or less than $50,050 annually.
However, since the calculated t-value of 1.0 does not fall within the critical region, we fail to reject the null hypothesis. Therefore, we cannot conclude that the welders earn either more or less than $50,050 annually.