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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.RS.3
Chapter 7, Problem 7.RS.3

You want your test to support a positive claim about your college, not just fail to reject one. Should you state your claim so that the null hypothesis contains the claim or the alternate hypothesis contains the claim? Explain.
Bar graph showing college costs, including tuition and financial aid amounts, with labeled categories and dollar values.

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Step 1: Understand the purpose of hypothesis testing. Hypothesis testing is used to make inferences about a population based on sample data. The null hypothesis (H₀) represents the status quo or no effect, while the alternative hypothesis (H₁) represents the claim or effect you want to support.
Step 2: Recognize the goal of the test. Since you want to support a positive claim about your college, the claim should be placed in the alternative hypothesis (H₁). This is because rejecting the null hypothesis (H₀) provides evidence in favor of the alternative hypothesis (H₁).
Step 3: Formulate the hypotheses. For example, if the claim is that the average grant and scholarship aid is greater than \$13,690, the null hypothesis (H₀) would state that the average aid is less than or equal to \$13,690, while the alternative hypothesis (H₁) would state that the average aid is greater than \$13,690.
Step 4: Choose the appropriate test and significance level. Depending on the data available, you might use a t-test or z-test to compare the sample mean to the hypothesized mean. Select a significance level (e.g., α = 0.05) to determine the threshold for rejecting the null hypothesis.
Step 5: Interpret the results. If the test statistic falls in the rejection region (or the p-value is less than α), you reject the null hypothesis (H₀) and conclude that there is sufficient evidence to support the positive claim about your college.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position in hypothesis testing. It is typically formulated to be tested against an alternative hypothesis. In this context, if you want to support a positive claim about your college, the null hypothesis would not contain this claim, as it represents the status quo or a lack of evidence for the claim.
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Step 1: Write Hypotheses

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that reflects the claim or effect that the researcher aims to support. It is the hypothesis that is accepted if the null hypothesis is rejected. In this scenario, stating your claim in the alternative hypothesis allows you to test for evidence that supports your positive assertion about the college.
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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a claim based on sample data. It involves comparing the null and alternative hypotheses using a significance level to determine whether to reject the null hypothesis. Understanding this process is crucial for effectively framing your claim and interpreting the results of your test.
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Related Practice
Textbook Question

In Exercises 7–10, explain how you should interpret a decision that fails to reject 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

[APPLET] A researcher claims that the mean age of the residents of a small town is more than 38 years. The ages (in years) of a random sample of 30 residents are listed below. At α=0.10, is there enough evidence to support the researcher’s claim? Assume the population standard deviation is 9 years.


Textbook Question

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.


Two-tailed test, z = 2.57, α = 0.10

Textbook Question

When you reject a true claim with a level of significance that is virtually zero, what can you infer about the randomness of your sampling process?

Textbook Question

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


σ > 1.9

Textbook Question

A travel analyst says that the mean price of a meal for a family of 4 in a resort restaurant is at most \$100. A random sample of 33 meal prices for families of 4 has a mean of \$110 and a standard deviation of \$19. At α=0.01, is there enough evidence to reject the analyst’s claim?