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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2:13 minutes

Problem 7.2.7

Textbook Question

Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.

P = 0.0838

Verified step by step guidance

Step 1: Recall the decision rule for hypothesis testing. If the P-value is less than or equal to the level of significance (α), reject the null hypothesis (H₀). Otherwise, fail to reject H₀.

Step 2: Compare the given P-value (P = 0.0838) to the first level of significance, α = 0.01. Determine whether P ≤ α or P > α.

Step 3: Compare the given P-value (P = 0.0838) to the second level of significance, α = 0.05. Determine whether P ≤ α or P > α.

Step 4: Compare the given P-value (P = 0.0838) to the third level of significance, α = 0.10. Determine whether P ≤ α or P > α.

Step 5: Based on the comparisons in Steps 2, 3, and 4, state whether to reject or fail to reject H₀ for each level of significance (α = 0.01, 0.05, and 0.10).

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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 results at least as extreme as the observed results, assuming that the null hypothesis (H0) is true. A lower P-value indicates stronger evidence against H0, while a higher P-value suggests weaker evidence.

Null Hypothesis (H0)

The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing. Researchers aim to gather evidence to either reject or fail to reject H0 based on the data collected. Understanding H0 is crucial for interpreting the results of a hypothesis test and the associated P-value.

Level of Significance (α)

The level of significance (α) is a threshold set by the researcher before conducting a hypothesis test, which determines the criteria for rejecting the null hypothesis. Common values for α are 0.01, 0.05, and 0.10. If the P-value is less than or equal to α, H0 is rejected; if it is greater, H0 is not rejected. This concept is essential for making informed decisions based on statistical evidence.

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Textbook Question

Explain the difference between the z-test for μ using a P-value and the z-test for μ using rejection region(s).

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Textbook Question

The mean of a random sample of 18 test scores is x_bar. The standard deviation of the population of all test scores is sigma= 6. Under what condition can you use a z-test to decide whether to reject a claim that the population mean is mu=88?

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Textbook Question

Hypothesis Testing Using Rejection Regions In Exercises 23–30, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic X^2, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.

Salaries The annual salaries (in dollars) of 15 randomly chosen senior level graphic design specialists are shown in the table at the left. At α=0.05, is there enough evidence to support the claim that the standard deviation of the annual salaries is different from $13,056?

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Textbook Question

In Exercises 7–10, (a) state the null and alternative hypotheses and identify which represents the claim.

A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900.

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Textbook Question

Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.

P = 0.0062

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Textbook Question

Can a critical value for the chi-square test be negative? Explain.

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Textbook Question

In Exercises 7–10, explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed. A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900.

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In Exercises 7–10, explain how you should interpret a decision that rejects the null hypothesis.

A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900.

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Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.P = 0.0838

Key Concepts

P-Value

Null Hypothesis (H0)

Level of Significance (α)

Watch next

Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.

P = 0.0838