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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1:36 minutes

Problem 7.1.22

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

Verified step by step guidance

Step 1: Understand the null hypothesis (H0) and the alternative hypothesis (Ha). In this case, H0: μ < 5.2 and Ha: μ ≥ 5.2.

Step 2: Recall that the direction of the test is determined by the alternative hypothesis (Ha). Specifically, the inequality in Ha indicates the type of test.

Step 3: Note that Ha: μ ≥ 5.2 includes the 'greater than or equal to' condition. This suggests that we are testing whether the mean (μ) is greater than or equal to 5.2.

Step 4: Since the focus is on testing whether μ is greater than a specific value (5.2), this is a right-tailed test. A right-tailed test is used when the alternative hypothesis involves a 'greater than' condition.

Step 5: Conclude that the hypothesis test is right-tailed based on the direction of the inequality in the alternative hypothesis (Ha).

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Key Concepts

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

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 a statement of no effect or no difference, and the alternative hypothesis (Ha), which represents what we aim to support. The outcome of the test helps determine whether to reject the null hypothesis in favor of the alternative.

One-Tailed vs. Two-Tailed Tests

In hypothesis testing, a one-tailed test evaluates the direction of the effect, either testing for an increase or a decrease, while a two-tailed test assesses for any significant difference in either direction. A left-tailed test looks for evidence that the parameter is less than a certain value, whereas a right-tailed test looks for evidence that it is greater. The choice between these tests depends on the research question and the hypotheses formulated.

Interpreting Hypotheses

Interpreting the null and alternative hypotheses is crucial for determining the type of test to conduct. In the given example, the null hypothesis (H0: μ < 5.2) suggests that the mean is less than 5.2, while the alternative hypothesis (Ha: μ ≥ 5.2) indicates that the mean is greater than or equal to 5.2. This setup implies a right-tailed test, as we are interested in whether the mean is significantly greater than 5.2.

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Textbook Question

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Unit Size A renters’ organization claims that the median number of rooms in renter-occupied units is four. You randomly select 120 renter-occupied units and obtain the results shown below. At , can you reject the organization’s claim? (Adapted from U.S. Census Bureau)

[IMAGE]

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Textbook Question

Hourly Wages A labor organization claims that the median hourly wage of podiatrists is at least $70.00. In a random sample of 23 podiatrists, 17 earn less than $70.00 per hour, 5 earn more than $70.00 per hour, and 1 earns $70.00 per hour. At , can you reject the labor organization’s claim? (Adapted from U.S. Bureau of Labor Statistics)

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Textbook Question

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.90, n = 8

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Textbook Question

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.

μ ≤ 645

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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.

Base Price of an ATV The standard deviation of the base price of an all-terrain vehicle is no more than $320.

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

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