Question

Pertains to performance information on tire sidewalls. Researchers aim to determine, at the 0.05 level of significance, whether there is evidence that the population mean tread wear index is less than 200. Formulate the appropriate null and alternative hypotheses:

H₀: The population mean tread wear index is at least 200.
Hₐ: The population mean tread wear index is less than 200.
Consider providing further details or context if necessary.

Answer 1

In statistical hypothesis testing for the mean tread wear index, the null hypothesis states the mean is at least 200, while the alternative hypothesis states it is less than 200. A p-value less than the significance level of 0.05 leads to the rejection of the null hypothesis in favor of the alternative.

Step-by-step explanation:

The question pertains to hypothesis testing in statistics, specifically testing whether the population mean tread wear index is less than 200. The appropriate null hypothesis (H₀) is that the population mean tread wear index is at least 200, which translates to H₀: μ ≥ 200. The alternative hypothesis (Hᵢ) is that the population mean tread wear index is less than 200, which is Hᵢ: μ < 200.

In hypothesis testing, if the p-value is less than the significance level (α), which is 0.05 in this case, the decision would be to reject the null hypothesis. Since the p-value is less than 0.05, there is sufficient evidence at the 5 percent significance level to reject the null hypothesis and accept the alternative hypothesis.

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