In Exercises 7–10, (a) state the null and alternative hypotheses and identify which represents the claim. A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than \$2900.
Verified step by step guidance
1
Step 1: Understand the context of the problem. The nonprofit consumer organization claims that the standard deviation of the starting prices of its top-rated vehicles is no more than \$2900. This means the claim is about the population standard deviation (σ).
Step 2: Define the null hypothesis (H₀). The null hypothesis represents the statement of no effect or no difference, and it often includes equality. In this case, H₀: σ ≤ 2900, as the claim is that the standard deviation is no more than \$2900.
Step 3: Define the alternative hypothesis (H₁). The alternative hypothesis represents the statement that contradicts the null hypothesis. Here, H₁: σ > 2900, as it challenges the claim by suggesting the standard deviation is greater than \$2900.
Step 4: Identify which hypothesis represents the claim. Since the claim is that the standard deviation is no more than \$2900, the null hypothesis (H₀: σ ≤ 2900) represents the claim.
Step 5: Summarize the hypotheses. The null hypothesis is H₀: σ ≤ 2900, and the alternative hypothesis is H₁: σ > 2900. The null hypothesis represents the claim made by the nonprofit consumer organization.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2m
Play a video:
0 Comments
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis
The null hypothesis (H0) is a statement that indicates no effect or no difference, serving as a default position in hypothesis testing. In this context, it asserts that the standard deviation of the starting prices of the vehicles is $2900 or less, suggesting that there is no significant variation in prices beyond this threshold.
The alternative hypothesis (H1) is a statement that contradicts the null hypothesis, indicating the presence of an effect or difference. For this scenario, it posits that the standard deviation of the starting prices exceeds $2900, representing the claim made by the nonprofit consumer organization that there is significant variability in vehicle prices.
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation suggests a wider spread of values. In this question, it is crucial for assessing the variability of starting prices among the top-rated vehicles.