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

Previous problemNext problem

2:02 minutes

Problem 7.RS.3

Textbook Question

You want your test to support a positive claim about your college, not just fail to reject one. Should you state your claim so that the null hypothesis contains the claim or the alternate hypothesis contains the claim? Explain.

Verified step by step guidance

Step 1: Understand the purpose of hypothesis testing. Hypothesis testing is used to make inferences about a population based on sample data. The null hypothesis (H₀) represents the status quo or no effect, while the alternative hypothesis (H₁) represents the claim or effect you want to support.

Step 2: Recognize the goal of the test. Since you want to support a positive claim about your college, the claim should be placed in the alternative hypothesis (H₁). This is because rejecting the null hypothesis (H₀) provides evidence in favor of the alternative hypothesis (H₁).

Step 3: Formulate the hypotheses. For example, if the claim is that the average grant and scholarship aid is greater than $13,690, the null hypothesis (H₀) would state that the average aid is less than or equal to $13,690, while the alternative hypothesis (H₁) would state that the average aid is greater than $13,690.

Step 4: Choose the appropriate test and significance level. Depending on the data available, you might use a t-test or z-test to compare the sample mean to the hypothesized mean. Select a significance level (e.g., α = 0.05) to determine the threshold for rejecting the null hypothesis.

Step 5: Interpret the results. If the test statistic falls in the rejection region (or the p-value is less than α), you reject the null hypothesis (H₀) and conclude that there is sufficient evidence to support the positive claim about your college.

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Key Concepts

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

Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position in hypothesis testing. It is typically formulated to be tested against an alternative hypothesis. In this context, if you want to support a positive claim about your college, the null hypothesis would not contain this claim, as it represents the status quo or a lack of evidence for the claim.

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that reflects the claim or effect that the researcher aims to support. It is the hypothesis that is accepted if the null hypothesis is rejected. In this scenario, stating your claim in the alternative hypothesis allows you to test for evidence that supports your positive assertion about the college.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a claim based on sample data. It involves comparing the null and alternative hypotheses using a significance level to determine whether to reject the null hypothesis. Understanding this process is crucial for effectively framing your claim and interpreting the results of your test.

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When the sign test is used, what population parameter is being tested?

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Describe the test statistic for the sign test when the sample size n is less than or equal to 25 and when n is greater than 25.

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Explain how to use the sign test to test a population median.

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Textbook Question

In Exercises 1–5, (a) identify the claim and state H0 and Ha, (b) decide which nonparametric test to use, (c) find the critical value(s), (d) find the test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim.

[APPLET] A meteorologist wants to determine whether days with rain occur randomly in April in his hometown. To do so, the meteorologist records whether it rains for each day in April. The results are shown, where R represents a day with rain and N represents a day with no rain. At , can the meteorologist conclude that days with rain are not random?

N R R N N N N R N R R N R R R

N R R R R N N N N R N R N N R

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Textbook Question

What are the conditions for using a Kruskal-Wallis test?

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Textbook Question

In your own words, explain why the hypothesis test discussed in this section is called the runs test.

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Textbook Question

In each exercise,

a. identify the claim and state H₀ and Hₐ,

In Exercises 1 and 2, use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups. (Adapted from U.S. Census Bureau)

Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use α=0.01.

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Textbook Question

In each exercise,

b. find the critical value and identify the rejection region,

Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use α=0.01.

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