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. IQ Scores Younger Sibling 83 102 89 97 100 105 96 91 94 77 Older Sibling 89 102 89 106 100 115 93 102 96 79 Assume a Normal distribution.  What can be concluded at the the αα = 0.01 level of significance? For this study, we should use Select an answer t-test for a population mean t-test for the difference between two independent population means z-test for a population proportion t-test for the difference between two dependent population means z-test for the difference between two population proportions  The null and alternative hypotheses would be:        H0:H0:  Select an answer μ1 p1 μd  Select an answer < > ≠ =  Select an answer p2 0 μ2  (please enter a decimal)     H1:H1:  Select an answer p1 μd μ1  Select an answer ≠ > = <  Select an answer p2 0 μ2  (Please enter a decimal) The test statistic ? t z  =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is ? ≤ >  αα Based on this, we should Select an answer reject accept fail to 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 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 ten younger siblings' IQ scores are not the same on average than the ten older siblings' IQ scores. Interpret the p-value in the context of the study. There is a 4.14% chance that the mean IQ score for the 10 younger siblings differs by at least 3.7 points from the mean IQ score for the 10 older siblings. There is a 4.14% chance of a Type I error. 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 4.14% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 3.7 points from the mean IQ score for the 10 older siblings. 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 4.14% chance that the mean IQ score for the 10 younger siblings would differ by at least 3.7 points from the mean IQ score for the 10 older siblings. Interpret the level of significance in the context of the study. There is a 1% chance that the population mean IQ score is the same for younger and 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 population mean IQ score for younger siblings is not the same as the population mean IQ score for older siblings 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.

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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.

IQ Scores

Younger Sibling 83 102 89 97 100 105 96 91 94 77
Older Sibling 89 102 89 106 100 115 93 102 96 79

Assume a Normal distribution.  What can be concluded at the the αα = 0.01 level of significance?

For this study, we should use Select an answer t-test for a population mean t-test for the difference between two independent population means z-test for a population proportion t-test for the difference between two dependent population means z-test for the difference between two population proportions 

  1. The null and alternative hypotheses would be:   
  2.   

 H0:H0:  Select an answer μ1 p1 μd  Select an answer < > ≠ =  Select an answer p2 0 μ2  (please enter a decimal)   

 H1:H1:  Select an answer p1 μd μ1  Select an answer ≠ > = <  Select an answer p2 0 μ2  (Please enter a decimal)

  1. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
  2. The p-value =  (Please show your answer to 4 decimal places.)
  3. The p-value is ? ≤ >  αα
  4. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
  5. 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 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 ten younger siblings' IQ scores are not the same on average than the ten older siblings' IQ scores.
  6. Interpret the p-value in the context of the study.
    • There is a 4.14% chance that the mean IQ score for the 10 younger siblings differs by at least 3.7 points from the mean IQ score for the 10 older siblings.
    • There is a 4.14% chance of a Type I error.
    • 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 4.14% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 3.7 points from the mean IQ score for the 10 older siblings.
    • 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 4.14% chance that the mean IQ score for the 10 younger siblings would differ by at least 3.7 points from the mean IQ score for the 10 older siblings.
  7. Interpret the level of significance in the context of the study.
    • There is a 1% chance that the population mean IQ score is the same for younger and 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 population mean IQ score for younger siblings is not the same as the population mean IQ score for older siblings
    • 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.
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