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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1:56 minutes

Problem 7.1.51a

Textbook Question

Writing Hypotheses: Backpack Manufacturer A backpack manufacturer claims that the mean life of its competitor’s backpacks is less than 5 years. You are asked to perform a hypothesis test to test this claim. How would you write the null and alternative hypotheses when

a. you represent the manufacturer and want to support the claim?

Verified step by step guidance

Understand the context: The manufacturer claims that the mean life of the competitor's backpacks is less than 5 years. This is a one-tailed hypothesis test because the claim is directional ('less than').

Define the null hypothesis (H₀): The null hypothesis always represents the status quo or no effect. In this case, it would state that the mean life of the competitor's backpacks is greater than or equal to 5 years. Mathematically, H₀: μ ≥ 5, where μ represents the mean life of the competitor's backpacks.

Define the alternative hypothesis (H₁): The alternative hypothesis represents the claim being tested. Since the manufacturer claims that the mean life is less than 5 years, the alternative hypothesis is H₁: μ < 5.

Verify the direction of the test: Since the alternative hypothesis uses '<', this is a left-tailed test. This will influence the critical region and p-value calculation during the hypothesis test.

Summarize the hypotheses: Null hypothesis (H₀): μ ≥ 5. Alternative hypothesis (H₁): μ < 5. These hypotheses will guide the statistical test to determine whether there is sufficient evidence to support the manufacturer's claim.

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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. In this context, it would assert that the mean life of the competitor's backpacks is equal to or greater than 5 years. This hypothesis is tested against the alternative hypothesis to determine if there is enough evidence to reject it.

Alternative Hypothesis (H1)

The alternative hypothesis represents the claim or effect that the researcher aims to support. In this scenario, it would state that the mean life of the competitor's backpacks is less than 5 years. This hypothesis is what the manufacturer wants to prove, and it is accepted if the evidence from the data is strong enough to reject the null hypothesis.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population 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. The process includes setting significance levels, collecting data, and interpreting results to draw conclusions about the claims being tested.

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Explain how to find critical values for a t-distribution.

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Textbook Question

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

a. rejects the null hypothesis?

A recent study claims that at least 20% of renters are behind on rent payments in New Jersey.

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Textbook Question

b. fails to reject the null hypothesis?

Rent A recent study claims that at least 20% of renters are behind on rent payments in New Jersey.

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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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Textbook Question

Writing Hypotheses: Backpack Manufacturer A backpack manufacturer claims that the mean life of its competitor’s backpacks is less than 5 years. You are asked to perform a hypothesis test to test this claim. How would you write the null and alternative hypotheses when

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

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Textbook Question

Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when

a. you represent the Internet provider and want to support the claim?

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Textbook Question

b. you represent a competing advertiser and want to reject the claim?

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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

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