Some research suggests that first born children may have higher IQ scores than their later born siblings. Do first-born identical twins have higher IQ scores than their second-born sibling? Data from a 1998 study were analyzed to determine whether first-born identical twins have higher IQ scores than their second-born siblings. Ten pairs of adult identical twins were assessed and their Full Scale IQ scores were calculated.Source: M. J. Tramo, W. C. Lodtus, T. A. Stukel, R. L. Green, J. B. Weaver, and M. S. Gazzaniga. “Brain Size, Head Size, and Intelligence Quotient in Monozygotic Twins.” Neurology 50, 1246–52.The following hypotheses were tested:H0: μd = 0Ha: μd < 0The following is the (edited) output for the test:SampleNMeanStDevSE MeanFirst-born10112.914.74.65Second-born10108.711.33.57Difference104.113.44.2395% lower bound for mean difference: −4.36t-test of mean difference = 0 (vs. > 0): t-value = 0.97, p-value = 0.179Which of the following is an appropriate conclusion based on the output? The data provide sufficient evidence to reject H0and, thus, conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins. The data do not provide sufficient evidence to reject H0. We therefore conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins. The data provide sufficient evidence to reject H0. We therefore conclude the data do not provide evidence to conclude that the mean Full Scale IQ scores for first-born identical twins is higher than that of second-born identical twins. The data do not provide sufficient evidence to reject H0. In other words, based on the data we cannot conclude that the mean Full Scale IQ scores for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.
Question
Some research suggests that first born children may have higher IQ scores than their later born siblings. Do first-born identical twins have higher IQ scores than their second-born sibling? Data from a 1998 study were analyzed to determine whether first-born identical twins have higher IQ scores than their second-born siblings. Ten pairs of adult identical twins were assessed and their Full Scale IQ scores were calculated.Source: M. J. Tramo, W. C. Lodtus, T. A. Stukel, R. L. Green, J. B. Weaver, and M. S. Gazzaniga. “Brain Size, Head Size, and Intelligence Quotient in Monozygotic Twins.” Neurology 50, 1246–52.The following hypotheses were tested:H0: μd = 0Ha: μd < 0The following is the (edited) output for the test:SampleNMeanStDevSE MeanFirst-born10112.914.74.65Second-born10108.711.33.57Difference104.113.44.2395% lower bound for mean difference: −4.36t-test of mean difference = 0 (vs. > 0): t-value = 0.97, p-value = 0.179Which of the following is an appropriate conclusion based on the output? The data provide sufficient evidence to reject H0and, thus, conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins. The data do not provide sufficient evidence to reject H0. We therefore conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins. The data provide sufficient evidence to reject H0. We therefore conclude the data do not provide evidence to conclude that the mean Full Scale IQ scores for first-born identical twins is higher than that of second-born identical twins. The data do not provide sufficient evidence to reject H0. In other words, based on the data we cannot conclude that the mean Full Scale IQ scores for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.
Solution
The correct conclusion based on the output is: "The data do not provide sufficient evidence to reject H0. In other words, based on the data we cannot conclude that the mean Full Scale IQ scores for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins."
Here's why:
The null hypothesis (H0) is that the mean difference in IQ scores between first-born and second-born identical twins is zero (μd = 0). The alternative hypothesis (Ha) is that the mean difference is less than zero (μd < 0), suggesting that first-born twins have a lower IQ score.
The p-value is 0.179, which is greater than the common significance level of 0.05. This means that we do not have enough evidence to reject the null hypothesis. In other words, we cannot conclude that first-born twins have a lower IQ score than their second-born siblings based on this data.
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