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.

Question

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.

Accepted Answer

Given Information:
Ten sibling pairs were given IQ tests.

Younger Sibling
91
88
88
91
114
100
110…