Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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1:59 minutes

Problem 7.1.49

Textbook Question

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?

Verified step by step guidance

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.

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.

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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b. you represent the competitor and want to reject the claim?

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