A myopenmath.com Question 3 5 pts 9 1 98 0 Details 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. Q Scores Younger Sibling 102 113 94 102 99 109 107 104 95 86 Older Sibling 102 108 108 104 98 108 110 112 97 88 Assume a Normal distribution. What can be concluded at the the a = 0.05 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer V Select an answer | Select an answer (please enter a decimal) H1 : Select an answer v Select an answer v Select an answer (Please enter a decimal) b. The test statistic (? = (please show your answer to 3 decimal places.) C. The p-value = (Please show your answer to 4 decimal places.) d. The p-value is ? a e. Based on this, we should ( Select an answer the null hypothesis. f. Thus, the final conclusion is that .. The results are statistically insignificant at a = 0.05, so there is insufficient evidence to conclude that the population mean IQ score for younger siblings is lower than the population meag IQ score for older siblings. The results are statistically significant at a = 0.05, 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 significant at a = 0.05, so there is sufficient evidence to conclude that the population mean IQ score for younger siblings is lower than the population mean IQ score or older siblings The results are statistically insignificant at o = 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. g. 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 9.2% chance of concluding that the mean IQ score for the 10 younger siblings is at least 2.4 points lower than the mean IQ score for the 10 older siblings. There is a 9.2% chance of a Type | 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 9.2% chance that the mean IQ score for the 10 younger siblings would be at least 2.4 points lower than the mean IQ score for the 10 older siblings. There is a 9.2%% chance that the mean IQ score for the 10 younger siblings is at least 2.4 points lower than the mean IQ score for the 10 older siblings. h. 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 sample mean IQ scores for these 10 sibling pairs differ from each other. 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 lower than the population mean IQ score for older siblings There is a 5% chance that the population mean IQ score is the same for younger and older siblings
