Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
         
a. rejects the null hypothesis?


Marketing A fitness equipment company claims that its competitor’s home gym does not have a customer satisfaction rate of 99%.

Verified step by step guidance

1. Step 1: Understand the problem. The fitness equipment company is making a claim about the customer satisfaction rate of its competitor's home gym. Specifically, the claim is that the satisfaction rate is not 99%. This is a two-tailed hypothesis test because the claim involves a 'not equal to' condition.
2. Step 2: Define the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis represents the default assumption, which is that the satisfaction rate is equal to 99%. Mathematically, H₀: p = 0.99. The alternative hypothesis represents the claim being tested, which is that the satisfaction rate is not 99%. Mathematically, Hₐ: p ≠ 0.99.
3. Step 3: Interpret the decision to reject the null hypothesis. If the null hypothesis is rejected, it means there is sufficient evidence to support the alternative hypothesis. In this context, rejecting H₀ would suggest that the competitor's home gym does not have a customer satisfaction rate of 99%.
4. Step 4: Interpret the decision to fail to reject the null hypothesis. If the null hypothesis is not rejected, it means there is not enough evidence to support the alternative hypothesis. In this case, it would suggest that the data does not provide sufficient evidence to conclude that the satisfaction rate is different from 99%.
5. Step 5: Summarize the implications of the hypothesis test. The decision to reject or fail to reject the null hypothesis depends on the test statistic and the significance level (α). Ensure that the test is conducted properly, and interpret the results in the context of the claim made by the fitness equipment company.

Key Concepts

Null Hypothesis

The null hypothesis (H0) is a statement that indicates no effect or no difference, serving as a default position in hypothesis testing. In this context, it would assert that the competitor's home gym does indeed have a customer satisfaction rate of 99%. The null hypothesis is tested against the alternative hypothesis to determine if there is enough evidence to reject it.

Alternative Hypothesis

The alternative hypothesis (H1) represents a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. In this case, the alternative hypothesis would claim that the competitor's home gym does not have a customer satisfaction rate of 99%. This hypothesis is what the fitness equipment company is trying to support through their claim.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a hypothesis based on sample data. When a hypothesis test is performed, a decision is made to either reject the null hypothesis or fail to reject it. Rejecting the null hypothesis indicates that there is sufficient evidence to support the alternative hypothesis, suggesting that the competitor's claim may not hold true.