On average is the younger sibling's IQ lower than the older sibling's IQ? Ten sibling pairs were given IQ tests. The data are shown below. IQ Scores Younger Sibling 91 87 110 104 111 100 92 98 119 105 Older Sibling
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
On average is the younger sibling's IQ lower than the older sibling's IQ? Ten sibling pairs were given IQ tests. The data are shown below.
IQ Scores
| Younger Sibling | 91 | 87 | 110 | 104 | 111 | 100 | 92 | 98 | 119 | 105 |
|---|---|---|---|---|---|---|---|---|---|---|
| Older Sibling | 102 | 90 | 121 | 117 | 121 | 103 | 98 | 111 | 137 | 98 |
Assume a
For this study, we should use
- The null and alternative hypotheses would be:
H0:H0: (please enter a decimal)
H1:H1: (Please enter a decimal)
- The test statistic = (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 the null hypothesis.
- Thus, the final conclusion is that ...
- The results are statistically insignificant at αα = 0.10, 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 = 0.10, so there is sufficient evidence to conclude that the population mean IQ score for younger siblings is lower than the population mean IQ score for older siblings
- The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the ten younger siblings' IQ scores are lower on average than the ten older siblings' IQ scores.
- The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean IQ score for younger siblings is lower than the population mean IQ score for older siblings.
- The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population
- Interpret the p-value in the context of the study.
- There is a 0.28% chance that the mean IQ score for the 10 younger siblings is at least 8.1 points lower than the mean IQ score for the 10 older siblings.
- 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 0.28% chance of concluding that the mean IQ score for the 10 younger siblings is at least 8.1 points lower than the mean IQ score for the 10 older siblings.
- There is a 0.28% chance of a Type I error.
- 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 0.28% chance that the mean IQ score for the 10 younger siblings would be at least 8.1 points lower than the mean IQ score for the 10 older siblings.
- Interpret the level of significance in the context of the study.
- 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 10% chance that we would end up falsely concuding that the population mean IQ score for younger siblings is lower than the population mean IQ score for older siblings
-
- There is a 10% chance that you are so much smarter than your sibling that there is no need to take an IQ test to make a comparison.
- There is a 10% chance that the population mean IQ score is the same for younger and 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 10% chance that we would end up falsely concuding that the sample mean IQ scores for these 10 sibling pairs differ from each other.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 1 images
