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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 7.1.49
Chapter 7, Problem 7.1.49

Writing Hypotheses: Medicine A medical research team is investigating the mean cost of a 30-day supply of a heart medication. A pharmaceutical company thinks that the mean cost is less than \$60. You want to support this claim. How would you write the null and alternative hypotheses?

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Understand the context: The null hypothesis (H₀) represents the default or status quo assumption, while the alternative hypothesis (Hₐ) represents the claim you want to support. In this case, the pharmaceutical company claims that the mean cost is less than \$60.
Define the population parameter: Let μ represent the mean cost of a 30-day supply of the heart medication.
Write the null hypothesis (H₀): The null hypothesis assumes that the mean cost is not less than \$60. Mathematically, this is written as H₀: μ ≥ 60.
Write the alternative hypothesis (Hₐ): The alternative hypothesis supports the claim that the mean cost is less than \$60. Mathematically, this is written as Hₐ: μ < 60.
Verify the hypotheses: Ensure that the null and alternative hypotheses are mutually exclusive and collectively exhaustive, meaning they cover all possible scenarios for the mean cost (μ).

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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 that there is no relationship between two measured phenomena. In this context, it would assert that the mean cost of the heart medication is equal to or greater than $60, which the pharmaceutical company is trying to challenge.
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Step 1: Write Hypotheses

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. In this scenario, the alternative hypothesis would claim that the mean cost of the heart medication is less than $60, which is the assertion the medical research team aims to support.
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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a hypothesis based on sample data. It involves calculating a test statistic and comparing it to a critical value to determine whether to reject the null hypothesis in favor of the alternative hypothesis, thus providing evidence for the claim being investigated.
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Related Practice
Textbook Question

Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.


Left-tailed test, α = 0.09

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Textbook Question

Finding a P-Value In Exercises 13–18, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance alpha.

Left-tailed test


z=-1.68

alpha=0.05

127
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Textbook Question

Graphical Analysis In Exercises 21 and 22, state whether each standardized test statistic z allows you to reject the null hypothesis. Explain your reasoning.


a. z = -1.301

b. z = 1.203

c. z = 1.280

d. z = 1.286


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Textbook Question

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.


Phone Repairs A cell phone repair shop advertises that the mean cost of repairing a phone screen is less than \$120.

216
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Textbook Question

In Exercises 15–22, test the claim about the population variance or standard deviation at the level of significance Assume the population is normally distributed.

Claim: σ^2>19, α=0.1. Sample statistics: s^2=28, n=17

54
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Textbook Question

In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.

Right-tailed test, α=0.05, n=23

77
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