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Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblem 7.RE.9a
Chapter 7, Problem 7.RE.9a

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.

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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.

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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.
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Step 1: Write Hypotheses

Alternative Hypothesis

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.
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Step 1: Write Hypotheses

Standard Deviation

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.
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Calculating Standard Deviation
Related Practice
Textbook Question

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.


Left-tailed test, α=0.05, n=48

Textbook Question

In Exercises 7–10, explain how you should interpret a decision that rejects the null hypothesis.


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.

Textbook Question

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


μ ≠ 150,020

Textbook Question

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


μ = 82

Textbook Question

In Exercises 7–10, describe type I and type II errors for a hypothesis test of the claim.


An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

Textbook Question

In Exercises 7–10, explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed. 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.