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 103 107 92 105 101 99 100 88 93 98 Sibling Older 103 113 100 112 108 113 121 97 90 99 Sibling 4 Assume a Normal distribution. What can be concluded at the the a = 0.01 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer ✓ Select an answer Select an answer (please enter a decimal) H₁: Select an answer ✓ Select an answer ✓ Select an answer (Please enter a decimal) = (please show your answer to 3 decimal places.) b. The test statistic c. The p-value = (Please show your answer to 4 decimal places.)
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 103 107 92 105 101 99 100 88 93 98 Sibling Older 103 113 100 112 108 113 121 97 90 99 Sibling 4 Assume a Normal distribution. What can be concluded at the the a = 0.01 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer ✓ Select an answer Select an answer (please enter a decimal) H₁: Select an answer ✓ Select an answer ✓ Select an answer (Please enter a decimal) = (please show your answer to 3 decimal places.) b. The test statistic c. The p-value = (Please show your answer to 4 decimal places.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Question
Transcribed Image Text:**Assessing the Difference in IQ Between Siblings**
**Study Scenario:**
On average, is the younger sibling's IQ different from the older sibling's IQ? Ten pairs of siblings were given IQ tests, and their scores are shown below:
**IQ Scores Table:**
| | Younger Sibling | Older Sibling |
|-----|-----------------|---------------|
| Pair 1 | 103 | 103 |
| Pair 2 | 107 | 113 |
| Pair 3 | 92 | 100 |
| Pair 4 | 105 | 112 |
| Pair 5 | 101 | 108 |
| Pair 6 | 99 | 113 |
| Pair 7 | 100 | 121 |
| Pair 8 | 88 | 97 |
| Pair 9 | 93 | 90 |
| Pair 10| 98 | 99 |
**Statistical Analysis:**
Assume a Normal distribution. The goal is to determine whether the IQ of younger siblings is significantly different from that of older siblings at the \(\alpha = 0.01\) level of significance.
**Hypothesis Testing:**
**a. Hypothesis Formulation:**
- The null and alternative hypotheses (H₀ and H₁) are formulated as follows:
- \(H_0\): There is no difference in IQ between younger and older siblings.
- \(H_1\): There is a significant difference in IQ between younger and older siblings.
**b. Calculations:**
- **Test Statistic:** This is calculated based on the IQ scores provided. (Please show your answer to three decimal places.)
- **P-value:** Determine the p-value corresponding to the test statistic obtained. (Please show your answer to four decimal places.)
**Purpose:**
This example demonstrates how to frame a hypothesis test, how to calculate relevant statistics, and how to interpret results to draw conclusions regarding the difference in IQ between younger and older siblings.
**Note:** Use appropriate statistical tools or software to compute the test statistic and p-value. Ensure your calculations are conducted with accuracy and precision to provide meaningful conclusions.
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