5.22 Getting enough sleep. 400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically significant difference from 50%, and use a significance level of 0.01.

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### Statistical Hypothesis Testing Exercises

#### 5.21 Minimum Wage, Part I
A Rasmussen Reports survey of 1,000 US adults investigates whether a majority believe that raising the minimum wage will positively affect the economy. Conduct a hypothesis test with a significance level of 0.01 to determine if the majority supports the claim.

#### 5.22 Getting Enough Sleep
This study involved 400 students, where 204 students reported they did not get enough sleep. The task is to conduct a hypothesis test to determine if this represents a significant difference from 50%. Use a significance level of your choice.

#### 5.23 Working Backwards, Part I
In a large university, 289 students randomly sampled indicated that they supported a specific measure. Conduct a hypothesis test with the following hypotheses:
- \(H_0: p = 0.3\)
- \(H_A: p \neq 0.3\)

Determine if the hypothesis is statistically significant.

#### 5.24 Working Backwards, Part II
Given a sample size of 300, determine the necessary sample proportion that equates the p-value to 0.05. Assume that all conditions necessary for statistical inference are satisfied.

### Analysis and Concepts
These exercises revolve around using hypothesis testing to analyze survey data. You'll need to:
- Formulate null and alternative hypotheses.
- Determine appropriate significance levels.
- Conduct tests for statistical significance.
- Interpret p-values to conclude whether to reject or accept the null hypothesis.

Each exercise requires a nuanced understanding of the conditions and steps required for hypothesis testing. Engage with these exercises to enhance your statistical analysis skills.
Transcribed Image Text:### Statistical Hypothesis Testing Exercises #### 5.21 Minimum Wage, Part I A Rasmussen Reports survey of 1,000 US adults investigates whether a majority believe that raising the minimum wage will positively affect the economy. Conduct a hypothesis test with a significance level of 0.01 to determine if the majority supports the claim. #### 5.22 Getting Enough Sleep This study involved 400 students, where 204 students reported they did not get enough sleep. The task is to conduct a hypothesis test to determine if this represents a significant difference from 50%. Use a significance level of your choice. #### 5.23 Working Backwards, Part I In a large university, 289 students randomly sampled indicated that they supported a specific measure. Conduct a hypothesis test with the following hypotheses: - \(H_0: p = 0.3\) - \(H_A: p \neq 0.3\) Determine if the hypothesis is statistically significant. #### 5.24 Working Backwards, Part II Given a sample size of 300, determine the necessary sample proportion that equates the p-value to 0.05. Assume that all conditions necessary for statistical inference are satisfied. ### Analysis and Concepts These exercises revolve around using hypothesis testing to analyze survey data. You'll need to: - Formulate null and alternative hypotheses. - Determine appropriate significance levels. - Conduct tests for statistical significance. - Interpret p-values to conclude whether to reject or accept the null hypothesis. Each exercise requires a nuanced understanding of the conditions and steps required for hypothesis testing. Engage with these exercises to enhance your statistical analysis skills.
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