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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2:47 minutes

Problem 7.2.26

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.

Right-tailed test, α = 0.08

Verified step by step guidance

Step 1: Understand the problem. This is a right-tailed z-test with a significance level (α) of 0.08. A right-tailed test means the rejection region is in the right tail of the standard normal distribution.

Step 2: Recall the relationship between the significance level (α) and the critical value. The critical value is the z-score that corresponds to the cumulative probability of 1 - α in the standard normal distribution.

Step 3: Use a z-table or statistical software to find the z-score that corresponds to a cumulative probability of 1 - α = 1 - 0.08 = 0.92. This z-score is the critical value for the test.

Step 4: Define the rejection region. For a right-tailed test, the rejection region consists of all z-scores greater than the critical value. This means if the test statistic falls in this region, you reject the null hypothesis.

Step 5: Visualize the rejection region on a standard normal distribution graph. Mark the critical value on the horizontal axis, shade the area to the right of this value to represent the rejection region, and label the area as α = 0.08.

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Key Concepts

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

Critical Value

A critical value is a point on the scale of the test statistic beyond which we reject the null hypothesis. In hypothesis testing, it is determined based on the significance level (α) and the type of test (one-tailed or two-tailed). For a right-tailed test, the critical value corresponds to the z-score that marks the threshold for the upper tail of the distribution.

Rejection Region

The rejection region is the range of values for the test statistic that leads to the rejection of the null hypothesis. In a right-tailed test, this region is located to the right of the critical value. It represents the area under the curve where the probability of observing a test statistic is less than the significance level (α), indicating that the observed result is statistically significant.

Level of Significance (α)

The level of significance, denoted as α, is the probability of rejecting the null hypothesis when it is actually true (Type I error). It is a threshold set by the researcher before conducting the test, commonly used values are 0.05, 0.01, and in this case, 0.08. The choice of α influences the critical value and the size of the rejection region, impacting the test's sensitivity.

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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

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 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

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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

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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Textbook Question

Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic X^2 allows you to reject the null hypothesis. Explain.

a. X^2=2.091

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Textbook Question

Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic X^2 allows you to reject the null hypothesis. Explain.

b. X^2=23.309