The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis? A) H₁: π ≠ $50,000 B) H₁: µ ≠ $50,000 C) H₁: µ

Question

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis? A) H₁: π ≠ $50,000 B) H₁: µ ≠ $50,000 C) H₁: µ < $50,000 D) H₁: µ = $50,000

Quizplus · Accepted Answer

The alternate hypothesis is a statement that contradicts the null hypothesis, which assumes the mean is equal to $50,000. Therefore, the alternate hypothesis should state that the mean is not equal to $50,000, which is option B. Option A is also incorrect because it only states that the mean is not equal to $50,000 but does not specify whether it is greater or less than $50,000. Option C is incorrect because it states that the mean is less than $50,000, which is not an appropriate alternate hypothesis given that we do not have any prior information or evidence to support such a claim. Option D is just a restatement of the null hypothesis and is not an alternate hypothesis.

The Mean Annual Incomes of Certified Welders Are Normally Distributed