MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Title: Understanding Hypothesis Testing in Movie-Going Habits**

**Introduction:**
This educational content explores a hypothesis test concerning the average number of movies watched by moviegoers. A moviegoer is defined as someone who watches at least one movie in a theater over a 12-month period. We examine whether a sample mean differs significantly from a known national average.

**Problem Statement:**
The average moviegoer sees 8.5 movies per year. A sample of 42 moviegoers from a large university reported an average of 10.2 movies per year. Given a population standard deviation of 3.2 movies, we will perform a hypothesis test at the 0.01 level of significance to determine if this difference is significant.

**Part 1 of 5: Stating the Hypotheses**

1. **Null Hypothesis (H₀):** μ = 8.5; the average number of movies watched is 8.5.
2. **Alternative Hypothesis (H₁):** μ ≠ 8.5; the average number of movies watched is not 8.5.

This scenario requires a two-tailed test, which checks if the sample mean is significantly different, either higher or lower, than the population mean.

**Part 2 of 5: Critical Values**

- To find the critical value(s), calculations must be rounded to at least two decimal places. Should there be multiple critical values, they should be separated by commas.

**Note on Graphs/Diagrams:**
- This segment does not include specific graphs or diagrams. However, in a typical educational setting, Z-distribution tables or graphs illustrating the two-tailed hypothesis test would be helpful in visualizing the critical regions.

This educational example guides students in understanding the process of hypothesis testing using real-world data and statistical reasoning.
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Transcribed Image Text:**Title: Understanding Hypothesis Testing in Movie-Going Habits** **Introduction:** This educational content explores a hypothesis test concerning the average number of movies watched by moviegoers. A moviegoer is defined as someone who watches at least one movie in a theater over a 12-month period. We examine whether a sample mean differs significantly from a known national average. **Problem Statement:** The average moviegoer sees 8.5 movies per year. A sample of 42 moviegoers from a large university reported an average of 10.2 movies per year. Given a population standard deviation of 3.2 movies, we will perform a hypothesis test at the 0.01 level of significance to determine if this difference is significant. **Part 1 of 5: Stating the Hypotheses** 1. **Null Hypothesis (H₀):** μ = 8.5; the average number of movies watched is 8.5. 2. **Alternative Hypothesis (H₁):** μ ≠ 8.5; the average number of movies watched is not 8.5. This scenario requires a two-tailed test, which checks if the sample mean is significantly different, either higher or lower, than the population mean. **Part 2 of 5: Critical Values** - To find the critical value(s), calculations must be rounded to at least two decimal places. Should there be multiple critical values, they should be separated by commas. **Note on Graphs/Diagrams:** - This segment does not include specific graphs or diagrams. However, in a typical educational setting, Z-distribution tables or graphs illustrating the two-tailed hypothesis test would be helpful in visualizing the critical regions. This educational example guides students in understanding the process of hypothesis testing using real-world data and statistical reasoning.
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