On average is the younger sibling's IQ higher than the older sibling's IQ? Ten sibling pairs were given IQ tests. The data are shown below.IQ ScoresYounger Sibling9188889111410011010010696Older Sibling8079908811485111989095Assume 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 dependent population means z-test for the difference between two population proportions z-test for a population proportion t-test for the difference between two independent population means The null and alternative hypotheses would be: H0:H0: Select an answer p1 μd μ1 Select an answer > ≠ = < Select an answer 0 μ2 p2 (please enter a decimal) H1:H1: Select an answer μd μ1 p1 Select an answer > ≠ < = Select an answer μ2 p2 0 (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 ? > ≤ ααBased on this, we should Select an answer fail to reject reject accept 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 ten younger siblings' IQ scores are higher 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 higher than 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 mean IQ score for younger siblings is higher than the population mean IQ score for older siblingsThe 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.Interpret the p-value in the context of the study.There is a 1.61% chance that the mean IQ score for the 10 younger siblings is at least 5.4 points higher than the mean IQ score for the 10 older siblings.There is a 1.61% 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 1.61% chance of concluding that the mean IQ score for the 10 younger siblings is at least 5.4 points higher than 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 1.61% chance that the mean IQ score for the 10 younger siblings would be at least 5.4 points higher than the mean IQ score for the 10 older siblings.

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Description: On average is the younger sibling's IQ higher than the older sibling's IQ? Ten sibling pairs were given IQ tests. The data are shown below.IQ ScoresYounger Sibling9188889111410011010010696Older Sibling8079908811485111989095Assume a Normal distributio

Given Information: Ten sibling pairs were given IQ tests. Younger Sibling 91 88 88 91 114 100 110…

Answered: On average is the younger sibling's IQ…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Problem 1P

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On average is the younger sibling's IQ higher than the older sibling's IQ? Ten sibling pairs were given IQ tests. The data are shown below.

IQ Scores

Younger Sibling	91	88	88	91	114	100	110	100	106	96
Older Sibling	80	79	90	88	114	85	111	98	90	95

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 dependent population means z-test for the difference between two population proportions z-test for a population proportion t-test for the difference between two independent population means

The null and alternative hypotheses would be:

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

H1:H1: Select an answer μd μ1 p1 Select an answer > ≠ < = Select an answer μ2 p2 0 (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 fail to reject reject accept 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 ten younger siblings' IQ scores are higher 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 higher than 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 mean IQ score for younger siblings is higher than 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.
Interpret the p-value in the context of the study.
- There is a 1.61% chance that the mean IQ score for the 10 younger siblings is at least 5.4 points higher than the mean IQ score for the 10 older siblings.
- There is a 1.61% 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 1.61% chance of concluding that the mean IQ score for the 10 younger siblings is at least 5.4 points higher than 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 1.61% chance that the mean IQ score for the 10 younger siblings would be at least 5.4 points higher than the mean IQ score for the 10 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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