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 77 115 100 97 108 102 108 87 108 98 Older Sibling 75 125 119 101 108 97 116 94 107 116 Assume a Normal distribution. What can be concluded at the the αα = 0.05 level of significance? 1. For this study, we should use Select an answer t-test for a population mean z-test for the difference between two population proportions z-test for a population proportion t-test for the difference between two dependent population means t-test for the difference between two independent population means 2. The null and alternative hypotheses would be: H0: Select an answer μd μ1 p1 Select an answer < ≠ = > Select an answer: 0, μ2, or p2 (please enter a decimal) H1: Select an answer μ1, p1, or μd Select an answer = > ≠ < Select an answer μ2, 0, p2 (Please enter a decimal) 3. The test statistic ? t or z =______ (please show your answer to 3 decimal places.) 4. The p-value =________ (Please show your answer to 4 decimal places.) 5. The p-value is ? ≤ or > 6. Based on this, we should? Select an answer fail to reject? reject? or accept? the null hypothesis. 7. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.05, 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 = 0.05, 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 significant at αα = 0.05, 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 = 0.05, 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. 8. Interpret the p-value in the context of the study. 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 5.26% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 5.8 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 5.26% chance that the mean IQ score for the 10 younger siblings would differ by at least 5.8 points from the mean IQ score for the 10 older siblings. There is a 5.26% chance that the mean IQ score for the 10 younger siblings differs by at least 5.8 points from the mean IQ score for the 10 older siblings. There is a 5.26% chance of a Type I error. 9. Interpret the level of significance in the context of the study. There is a 5% 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 5% 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 5% 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 5% chance that the population mean IQ score is the same for younger and older siblings.

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 77 115 100 97 108 102 108 87 108 98 Older Sibling 75 125 119 101 108 97 116 94 107 116 Assume a Normal distribution. What can be concluded at the the αα = 0.05 level of significance? 1. For this study, we should use Select an answer t-test for a population mean z-test for the difference between two population proportions z-test for a population proportion t-test for the difference between two dependent population means t-test for the difference between two independent population means 2. The null and alternative hypotheses would be: H0: Select an answer μd μ1 p1 Select an answer < ≠ = > Select an answer: 0, μ2, or p2 (please enter a decimal) H1: Select an answer μ1, p1, or μd Select an answer = > ≠ < Select an answer μ2, 0, p2 (Please enter a decimal) 3. The test statistic ? t or z = (please show your answer to 3 decimal places.) 4. The p-value =__ (Please show your answer to 4 decimal places.) 5. The p-value is ? ≤ or > 6. Based on this, we should? Select an answer fail to reject? reject? or accept? the null hypothesis. 7. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.05, 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 = 0.05, 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 significant at αα = 0.05, 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 = 0.05, 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. 8. Interpret the p-value in the context of the study. 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 5.26% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 5.8 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 5.26% chance that the mean IQ score for the 10 younger siblings would differ by at least 5.8 points from the mean IQ score for the 10 older siblings. There is a 5.26% chance that the mean IQ score for the 10 younger siblings differs by at least 5.8 points from the mean IQ score for the 10 older siblings. There is a 5.26% chance of a Type I error. 9. Interpret the level of significance in the context of the study. There is a 5% 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 5% 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 5% 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 5% chance that the population mean IQ score is the same for younger and older siblings.

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	77	115	100	97	108	102	108	87	108	98
Older Sibling	75	125	119	101	108	97	116	94	107	116

Assume a Normal distribution. What can be concluded at the the αα = 0.05 level of significance?

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

2. The null and alternative hypotheses would be:

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

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

3. The test statistic ? t or z =______ (please show your answer to 3 decimal places.)

4. The p-value =________ (Please show your answer to 4 decimal places.)

5. The p-value is ? ≤ or >

6. Based on this, we should? Select an answer fail to reject? reject? or accept? the null hypothesis.

7. Thus, the final conclusion is that ...

The results are statistically significant at αα = 0.05, 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 = 0.05, 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 significant at αα = 0.05, 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 = 0.05, 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.

8. Interpret the p-value in the context of the study.

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 5.26% chance of concluding that the mean IQ score for the 10 younger siblings differs by at least 5.8 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 5.26% chance that the mean IQ score for the 10 younger siblings would differ by at least 5.8 points from the mean IQ score for the 10 older siblings.
There is a 5.26% chance that the mean IQ score for the 10 younger siblings differs by at least 5.8 points from the mean IQ score for the 10 older siblings.
There is a 5.26% chance of a Type I error.

9. Interpret the level of significance in the context of the study.

There is a 5% 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 5% 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 5% 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 5% chance that the population mean IQ score is the same for younger and older siblings.

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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