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MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Text Transcription for Educational Purposes** **Title:** Analyzing the Average Number of Paintings in Teachers' Houses **Introduction:** The average house has 13 paintings on its walls. We want to determine if the mean is smaller for houses owned by teachers. This analysis is based on data from a survey of 15 teachers who were asked about the number of paintings in their houses. Assume that the distribution of the population is normal. **Data Collected:** 11, 13, 10, 12, 13, 12, 14, 14, 10, 14, 12, 13, 12, 14, 12 **Statistical Analysis at \(\alpha = 0.05\):** **Hypotheses:** - **a.** For this study, we use a hypothesis test. - **b.** - **Null Hypothesis (\(H_0\)):** The mean number of paintings in teachers' houses is **equal to 13**. - **Alternative Hypothesis (\(H_1\)):** The mean number of paintings in teachers' houses is **less than 13**. **Calculation:** - **c.** Test Statistic: \(t = -1.69\) (rounded to 2 decimal places). - **d.** P-value = **0.0539** (rounded to 4 decimal places). - **e.** Evaluate if the p-value \(> \alpha\). **Conclusion:** - **f.** Based on the p-value, we should **fail to reject** the null hypothesis. - **g.** The final conclusion is that the data suggest the population mean number of paintings in teachers' houses is **not significantly less than 13** at \(\alpha = 0.05\). Therefore, there is insufficient evidence to conclude that the population mean is less than 13. **Interpretation:** - **h.** If the population mean number of paintings in teachers' houses is 13 and an additional 15 teachers are surveyed, there is a **5.39% chance** that the population mean number of paintings in teachers' houses would be less than 13. **Visual Aids:** There are no graphs or diagrams provided in this analysis. All information is conveyed through text and numerical data. **Summary:** This analysis explores whether teachers have fewer paintings
Transcribed Image Text:**Text Transcription for Educational Purposes** **Title:** Analyzing the Average Number of Paintings in Teachers' Houses **Introduction:** The average house has 13 paintings on its walls. We want to determine if the mean is smaller for houses owned by teachers. This analysis is based on data from a survey of 15 teachers who were asked about the number of paintings in their houses. Assume that the distribution of the population is normal. **Data Collected:** 11, 13, 10, 12, 13, 12, 14, 14, 10, 14, 12, 13, 12, 14, 12 **Statistical Analysis at \(\alpha = 0.05\):** **Hypotheses:** - **a.** For this study, we use a hypothesis test. - **b.** - **Null Hypothesis (\(H_0\)):** The mean number of paintings in teachers' houses is **equal to 13**. - **Alternative Hypothesis (\(H_1\)):** The mean number of paintings in teachers' houses is **less than 13**. **Calculation:** - **c.** Test Statistic: \(t = -1.69\) (rounded to 2 decimal places). - **d.** P-value = **0.0539** (rounded to 4 decimal places). - **e.** Evaluate if the p-value \(> \alpha\). **Conclusion:** - **f.** Based on the p-value, we should **fail to reject** the null hypothesis. - **g.** The final conclusion is that the data suggest the population mean number of paintings in teachers' houses is **not significantly less than 13** at \(\alpha = 0.05\). Therefore, there is insufficient evidence to conclude that the population mean is less than 13. **Interpretation:** - **h.** If the population mean number of paintings in teachers' houses is 13 and an additional 15 teachers are surveyed, there is a **5.39% chance** that the population mean number of paintings in teachers' houses would be less than 13. **Visual Aids:** There are no graphs or diagrams provided in this analysis. All information is conveyed through text and numerical data. **Summary:** This analysis explores whether teachers have fewer paintings
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