The manufacturer of an over-the-counter heartburn relief mediation claims that it product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the standard deviation was 1.1 minutes. Assume that time is normally distributed.
-The null and alternative hypotheses to test the manufacturer's claim is _____.

Question

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The null hypothesis (H0) is a statement of no effect or no difference, and it often represents a statement of equality (e.g., =). In this context, the null hypothesis would assert that the mean time to relief is equal to or greater than 3.5 minutes, as this is the benchmark the manufacturer wants to prove it can beat. The alternative hypothesis (Ha) is what the researcher aims to support, representing a statement of inequality (e.g., <, >). Here, the alternative hypothesis is that the mean time to relief is less than 3.5 minutes, which supports the manufacturer's claim. Therefore, the correct hypotheses to test the manufacturer's claim are H0: μ ≥ 3.5 vs. Ha: μ < 3.5.

The Manufacturer of an Over-The-Counter Heartburn Relief Mediation Claims That