Question

Determine the appropriate null and alternative hypotheses.

A. H₀ colon space the population mean tread wear index is at least 200.
Hₐ column space the population mean tread wear index is less than 200.
B. H₀ colon spacethe sample mean tread wear index is at least 200.
Hₐ colon spacethe sample mean tread wear index is less than 200.
C. H₀ colon spacethe sample proportion tread wear index is at least 200.
Hₐ colon spacethe sample proportion tread wear index is less than 200.
D. H₀ colon spacethe population proportion tread wear index is at least 200.
Hₐ colon spacethe population proportion tread wear index is less than 200.

Answer 1

The appropriate null and alternative hypotheses for a hypothesis test about a population mean are stated in terms of the population, not the sample. The correct hypotheses are that the population mean tread wear index is at least 200 (null) and less than 200 (alternative).

Step-by-step explanation:

To determine the appropriate null and alternative hypotheses, we should understand that null hypotheses typically state that there is no effect or no difference, and it usually contains an equality sign. The alternative hypothesis, on the other hand, suggests that there is an effect or a difference, and it reflects what we are trying to demonstrate through our testing.

For a hypothesis test about a population mean where the population standard deviation is known, the null hypothesis is generally stated in terms of the population parameter (not the sample statistic). Therefore, the correct null and alternative hypotheses should be framed in terms of the population mean, not the sample mean or proportion.

With this in mind, the correct option here is:

• H₀: The population mean tread wear index is at least 200.
• Hᵢ: The population mean tread wear index is less than 200.