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.

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.

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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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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