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 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
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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1:57 minutes

Problem 7.2

Textbook Question

In Exercise 1, you rejected the claim that p=0.53. But this claim was true. What type of error is this?

Verified step by step guidance

Understand the context: In hypothesis testing, there are two types of errors - Type I error and Type II error. A Type I error occurs when the null hypothesis is rejected even though it is true. A Type II error occurs when the null hypothesis is not rejected even though it is false.

Identify the null hypothesis (H₀): The null hypothesis in this case is that p = 0.53.

Analyze the situation: The problem states that you rejected the claim that p = 0.53, but this claim was actually true. This means you rejected a true null hypothesis.

Determine the type of error: Rejecting a true null hypothesis corresponds to a Type I error.

Conclude: The error made in this situation is a Type I error.

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Key Concepts

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

Type I Error

A Type I error occurs when a true null hypothesis is incorrectly rejected. In the context of hypothesis testing, this means concluding that there is an effect or difference when, in fact, there is none. This type of error is often denoted by the significance level alpha (α), which represents the probability of making this error.

Null Hypothesis (H0)

The null hypothesis is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing. In this case, the null hypothesis would state that the population proportion p is equal to 0.53. Researchers test this hypothesis against an alternative hypothesis to determine if there is enough evidence to reject it.

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship observed in data is not due to random chance. It is typically assessed using a p-value, which indicates the probability of observing the data if the null hypothesis is true. A result is considered statistically significant if the p-value is less than the predetermined significance level, often set at 0.05.

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Textbook Question

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: μ ≥ 5.2

H0: μ < 5.2

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Textbook Question

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: σ^2 = 142

H0: σ ≠ 142

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Textbook Question

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

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Textbook Question

A nutrition bar manufacturer claims that the standard deviation of the number of grams of carbohydrates in a bar is 1.11 grams. A random sample of 26 bars has a standard deviation of 1.19 grams. At α=0.05, is there enough evidence to reject the manufacturer’s claim? Assume the population is normally distributed.

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Textbook Question

In Exercises 55–58, test the claim about the population variance or standard deviation at the level of significance . Assume the population is normally distributed.

Claim: σ^2 > 2; α=0.10. Sample statistics: s^2 = 2.95, n=18

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Textbook Question

In Exercises 51–54, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance.

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Textbook Question

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.

Two-tailed test, α=0.02, n=12

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Textbook Question

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.