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g. Interpret the p-value in the context of the study. O f the population mean IQ score for younger siblings is the same as the population mean. IQ Score for older siblings and if another 10 sibling pairs are given an IQ test then there would be a 2.28% chance that the mean IQ score for the 10 younger siblings would differ by at least 4.5 points from the mean IQ score for the 10 older siblings. O There is a 2.28% chance that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. O If the sample mean IQ score for the 10 younger siblings is the same as the sample mean IQ score for the 10 older siblings and if another 10 sibling pairs are given an IQ test then there would be a 2.28% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. O There is a 2.28% chance of a Type I error. h. Interpret the level of significance in the context of the study. O If the population mean IQ score for younger siblings is the same as the population mean IQ Score for older siblings and if another 10 sibling pairs are given an J0 test, then there would be

g. Interpret the p-value in the context of the study. O f the population mean IQ score for younger siblings is the same as the population mean. IQ Score for older siblings and if another 10 sibling pairs are given an IQ test then there would be a 2.28% chance that the mean IQ score for the 10 younger siblings would differ by at least 4.5 points from the mean IQ score for the 10 older siblings. O There is a 2.28% chance that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. O If the sample mean IQ score for the 10 younger siblings is the same as the sample mean IQ score for the 10 older siblings and if another 10 sibling pairs are given an IQ test then there would be a 2.28% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. O There is a 2.28% chance of a Type I error. h. Interpret the level of significance in the context of the study. O If the population mean IQ score for younger siblings is the same as the population mean IQ Score for older siblings and if another 10 sibling pairs are given an J0 test, then there would be

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
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**Transcription of Image:** g. Interpret the p-value in the context of the study. - ○ If the population mean IQ score for younger siblings is the same as the population mean IQ score for older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 2.28% chance that the mean IQ score for the 10 younger siblings would differ by at least 4.5 points from the mean IQ score for the 10 older siblings. - ○ There is a 2.28% chance that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. - ○ If the sample mean IQ score for the 10 younger siblings is the same as the sample mean IQ score for the 10 older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 2.28% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. - ○ There is a 2.28% chance of a Type I error. h. Interpret the level of significance in the context of the study. - ○ If the population mean IQ score for younger siblings is the same as the population mean IQ score for older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 1% chance that we would end up falsely concluding that the population mean IQ score for younger siblings is not the same as the population mean IQ score for older siblings. - ○ There is a 1% chance that you are so much smarter than your sibling that there is no need to take an IQ test to make a comparison. - ○ If the population mean IQ score for younger siblings is the same as the population mean IQ score for older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 1% chance that we would end up falsely concluding that the sample mean IQ scores for these 10 sibling pairs differ from each other. - ○ There is a 1% chance that the population mean IQ score is the same for younger and older siblings.
Transcribed Image Text:**Transcription of Image:** g. Interpret the p-value in the context of the study. - ○ If the population mean IQ score for younger siblings is the same as the population mean IQ score for older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 2.28% chance that the mean IQ score for the 10 younger siblings would differ by at least 4.5 points from the mean IQ score for the 10 older siblings. - ○ There is a 2.28% chance that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. - ○ If the sample mean IQ score for the 10 younger siblings is the same as the sample mean IQ score for the 10 older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 2.28% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 4.5 points from the mean IQ score for the 10 older siblings. - ○ There is a 2.28% chance of a Type I error. h. Interpret the level of significance in the context of the study. - ○ If the population mean IQ score for younger siblings is the same as the population mean IQ score for older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 1% chance that we would end up falsely concluding that the population mean IQ score for younger siblings is not the same as the population mean IQ score for older siblings. - ○ There is a 1% chance that you are so much smarter than your sibling that there is no need to take an IQ test to make a comparison. - ○ If the population mean IQ score for younger siblings is the same as the population mean IQ score for older siblings and if another 10 sibling pairs are given an IQ test, then there would be a 1% chance that we would end up falsely concluding that the sample mean IQ scores for these 10 sibling pairs differ from each other. - ○ There is a 1% chance that the population mean IQ score is the same for younger and older siblings.
**Data Analysis for Sibling IQ Scores** This study examines the IQ scores of younger and older siblings, assuming a normal distribution. Below is the data collected: | Younger Sibling | Older Sibling | |-----------------|---------------| | 97 | 94 | | 85 | 92 | | 92 | 97 | | 111 | 115 | | 82 | 110 | | 101 | 103 | | 110 | 113 | | 112 | 125 | | 100 | 104 | **Statistical Analysis** **Objective:** Determine if there is a significant difference in the IQ scores between younger and older siblings at the α = 0.01 level of significance. 1. **Hypotheses:** - **Null Hypothesis (H₀):** There is no significant difference between the population mean IQ scores of younger and older siblings. - **Alternative Hypothesis (H₁):** There is a significant difference between the population mean IQ scores of younger and older siblings. 2. **Test Statistic:** - Calculated as -2.741. 3. **P-value:** - Obtained as 0.0228. 4. **Decision Rule:** - Compare the p-value to α (0.01). 5. **Conclusion:** - The p-value (0.0228) is greater than α (0.01). - Thus, we fail to reject the null hypothesis. **Final Conclusion:** - The results are statistically insignificant at α = 0.01, indicating insufficient evidence to conclude that the population mean IQ score for younger siblings is different from that for older siblings.
Transcribed Image Text:**Data Analysis for Sibling IQ Scores** This study examines the IQ scores of younger and older siblings, assuming a normal distribution. Below is the data collected: | Younger Sibling | Older Sibling | |-----------------|---------------| | 97 | 94 | | 85 | 92 | | 92 | 97 | | 111 | 115 | | 82 | 110 | | 101 | 103 | | 110 | 113 | | 112 | 125 | | 100 | 104 | **Statistical Analysis** **Objective:** Determine if there is a significant difference in the IQ scores between younger and older siblings at the α = 0.01 level of significance. 1. **Hypotheses:** - **Null Hypothesis (H₀):** There is no significant difference between the population mean IQ scores of younger and older siblings. - **Alternative Hypothesis (H₁):** There is a significant difference between the population mean IQ scores of younger and older siblings. 2. **Test Statistic:** - Calculated as -2.741. 3. **P-value:** - Obtained as 0.0228. 4. **Decision Rule:** - Compare the p-value to α (0.01). 5. **Conclusion:** - The p-value (0.0228) is greater than α (0.01). - Thus, we fail to reject the null hypothesis. **Final Conclusion:** - The results are statistically insignificant at α = 0.01, indicating insufficient evidence to conclude that the population mean IQ score for younger siblings is different from that for older siblings.
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