MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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On average is the younger sibling's IQ different from the older sibling's IQ? Ten sibling pairs were given IQ tests. The data are shown below.
Younger Sibling | 97 | 85 | 92 | 111 | 82 | 101 | 101 | 110 | 112 | 100 |
---|---|---|---|---|---|---|---|---|---|---|
Older Sibling | 94 | 92 | 97 | 115 | 80 | 113 | 103 | 113 | 125 | 104 |
Assume a
For this study, we should use
- The null and alternative hypotheses would be:
H0:H0: ud,p1p1/ >,>,=/ 0, p2,u2 (please enter a decimal)
H1:H1: ud,p1p1/ >,>,=/ 0, p2,u2 (Please enter a decimal)
- The test statistic z or t is -2.741. Enter it here (please show your answer to 3 decimal places.)
- The p-value is 0.0228. Enter it here (Please show your answer to 4 decimal places.)
- The p-value is <,> αα
- Based on this, we should accept , fail ro reject, or reject the null hypothesis.
- Thus, the final conclusion is that ...
- The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population
mean IQ score for younger siblings is not the same as the population mean IQ score for older siblings - The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the ten younger siblings' IQ scores are not the same on average than the ten older siblings' IQ scores.
- The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean IQ score for younger siblings is not the same as the population mean IQ score for older siblings.
- The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean IQ score for younger siblings is equal to the population mean IQ score for older siblings.
- The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population
- 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.
- 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 concuding 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 concuding 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.
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