Question

For the statement below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim.

The standard deviation of the base price of a certain type of all-terrain vehicle is no more than $336.
Write the claim as a mathematical statement.

Choose the correct null and alternative

Answer 1

The claim that the standard deviation of the base price of a certain type of all-terrain vehicle is no more than $336 is represented by the null hypothesis H0: σ ≤ $336. The alternative hypothesis is Ha: σ > $336, indicating this is a right-tailed test.

Step-by-step explanation:

When formulating a hypothesis test for the standard deviation of the base price of a certain type of all-terrain vehicle, the claim that the standard deviation is no more than $336 can be stated mathematically as:

σ ≤ $336

The null hypothesis (H0) represents no effect or no difference and would be the claim made in the statement:

H0: σ ≤ $336

The alternative hypothesis (Ha) represents the opposite of the null, suggesting there is an effect or a difference. In this case, the alternative hypothesis challenges the claim that the standard deviation is no more than $336:

Ha: σ > $336

This is a right-tailed test, as the alternative hypothesis is looking for evidence of the standard deviation being greater than a certain value.