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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1:54 minutes

Problem 7.2.18

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= 1.95
alpha=0.08

Verified step by step guidance

Step 1: Understand the problem. This is a left-tailed hypothesis test where the standardized test statistic z = 1.95, and the level of significance (α) is 0.08. The goal is to find the P-value and decide whether to reject the null hypothesis (H₀).

Step 2: Recall that the P-value in a left-tailed test is the area to the left of the given z-score on the standard normal distribution curve. Use a z-table, statistical software, or a calculator to find the cumulative probability corresponding to z = 1.95.

Step 3: Compare the P-value obtained in Step 2 to the level of significance α = 0.08. If the P-value is less than or equal to α, reject the null hypothesis (H₀). Otherwise, fail to reject H₀.

Step 4: Interpret the result. If the null hypothesis is rejected, it means there is sufficient evidence to support the alternative hypothesis at the given level of significance. If the null hypothesis is not rejected, it means there is insufficient evidence to support the alternative hypothesis.

Step 5: Summarize the decision. Clearly state whether H₀ is rejected or not based on the comparison between the P-value and α.

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Key Concepts

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

P-Value

The P-value is a statistical measure that helps determine the significance of results in hypothesis testing. It represents the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis (H0) is true. A smaller P-value indicates stronger evidence against H0, leading to a potential rejection of the null hypothesis.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents no effect or no difference, and the alternative hypothesis (H1), which represents the effect or difference. The outcome of the test helps determine whether to reject H0 in favor of H1.

Level of Significance (Alpha)

The level of significance, denoted as alpha (α), is the threshold for deciding whether to reject the null hypothesis. It represents the probability of making a Type I error, which occurs when H0 is incorrectly rejected. Common alpha levels are 0.05 and 0.01, but in this case, it is set at 0.08, meaning there is an 8% risk of rejecting H0 when it is actually true.

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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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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

Right-tailed test, α = 0.08

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Textbook Question

Two-tailed test, α = 0.12

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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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