Question

In preparation for upcoming wage negotiations with the union, the managers for the bevel hardware company want to establish the time required to assemble a kitchen cabinet. a first line supervisor believes that the job should take 50 minutes on average to complete. a random sample of 28 cabinets has an average assembly time of 55 minutes with a population standard deviation of 13 minutes. is there overwhelming evidence to contradict the first line supervisor’s belief at a 0.01 significance level? assume the population of assembly times is approximately normally distributed. step 1 of 3 : state the null and alternative hypotheses for the test. fill in the blank below. h0ha: μ=50:_____

Answer 1

The null hypothesis for the managers of the bevel hardware company is H0: μ=50, indicating no difference from the supervisor's belief of the average assembly time. The alternative hypothesis is Ha: μ≠50, which states that the actual time is different from 50 minutes.

Step-by-step explanation:

In preparation for wage negotiations, when the managers need to establish the average time required to assemble a kitchen cabinet, the first step is to declare the null (H0) and alternative hypotheses (Ha) for the statistical test.

The null hypothesis (H0) is a statement asserting that there is no effect or no difference, and it often represents a default position or a statement established based on theory or previous evidence. In this scenario, the null hypothesis states that the average time to assemble a cabinet is 50 minutes, hence H0: μ=50.

The alternative hypothesis (Ha), on the other hand, is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference that is worth noticing. In this case, it is not specifically stated whether the supervisor is concerned about times being higher or lower, or simply different from 50 minutes.

However, since we are asked if there's 'overwhelming evidence to contradict the supervisor's belief', we can assume we are looking for evidence that the time is different, not specifically higher or lower. Therefore, the alternative hypothesis is not one-sided but rather suggests that the actual assembly time is not 50 minutes, represented as Ha: μ ≠ 50.