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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

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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.

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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

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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

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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.

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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.

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