Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when


b. you represent a competing advertiser and want to reject the claim?

Verified step by step guidance

1. Step 1: Understand the context of the problem. The Internet provider claims that the mean time a customer spends online per day is greater than 28 minutes. This is a one-tailed hypothesis test because the claim specifies a direction ('greater than').
2. Step 2: Define the null hypothesis (H₀). The null hypothesis represents the status quo or the claim you want to test against. Since you are representing a competing advertiser and want to reject the provider's claim, the null hypothesis should state that the mean time a customer spends online per day is less than or equal to 28 minutes. Mathematically, H₀: μ ≤ 28, where μ is the population mean time spent online per day.
3. Step 3: Define the alternative hypothesis (H₁). The alternative hypothesis represents the claim you are testing for. In this case, since you want to reject the provider's claim, the alternative hypothesis should state that the mean time a customer spends online per day is not greater than 28 minutes. Mathematically, H₁: μ > 28.
4. Step 4: Write the hypotheses in symbolic form. Null hypothesis: H₀: μ ≤ 28. Alternative hypothesis: H₁: μ > 28. These hypotheses are written in terms of the population mean (μ).
5. Step 5: Verify the direction of the test. Since the alternative hypothesis (H₁) involves 'greater than,' this is a one-tailed test. This will influence the critical region and p-value calculation in subsequent steps of hypothesis testing.

Key Concepts

Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position that there is no relationship between two measured phenomena. In this context, it would assert that the mean time customers spend online per day is less than or equal to 28 minutes, which the internet provider claims is not true.

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For this scenario, as a competing advertiser, you would formulate the alternative hypothesis to state that the mean time customers spend online per day is less than 28 minutes, which directly challenges the provider's claim.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a hypothesis based on sample data. It involves calculating a test statistic and comparing it to a critical value to determine whether to reject the null hypothesis in favor of the alternative hypothesis, thus providing a framework for making inferences about population parameters.