Researchers studying IQ scores of mothers and fathers ofgifted" children collected data from 36 gifted children and their parents. First, differences in lQ scores of the father and the mother were calculated for each child (calculated as father's IQ score - mother's IQ score). The dot plot below shows the bootstrap distribution of means of 200 bootstrap samples taken from this original sample of differences in IQ scores. The mean of the bootstrap distribution is approximately -3.48 points and the bootstrap standard error is 1.3 points. Assume the usual conditions for constructing a bootstrap confidence interval are satisfied. Which of the following statements is false? -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 O A 95% bootstrap confidence interval for the difference in IQ scores is approximately (-6, -0.9). It's likely that in the original sample, most mothers had higher IQ scores than the fathers. O A 90% bootstrap confidence interval for the difference in IQ scores would is approximately (-5.6, -1.3). O Since 0 is apparently an unusual value for the statistic, then at the 5% significance level we would fail to reject a null hypothesis of that claims that the fathers' and mothers' average IQs are equal. •..

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4. Researchers studying IQ scores of mothers and fathers of `gifted" children collected data from 36 gifted children
and their parents. First, differences in IQ scores of the father and the mother were calculated for each child
(calculated as father's IQ score - mother's IQ score). The dot plot below shows the bootstrap distribution of means
of 200 bootstrap samples taken from this original sample of differences in IQ scores. The mean of the bootstrap
distribution is approximately -3.48 points and the bootstrap standard error is 1.3 points. Assume the usual
conditions for constructing a bootstrap confidence interval are satisfied. Which of the following statements is false?
-6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1
-0.5 0
0.5
1
O A 95% bootstrap confidence interval for the difference in IQ scores is approximately (-6, -0.9).
It's likely that in the original sample, most mothers had higher IQ scores than the fathers.
A 90% bootstrap confidence interval for the difference in IQ scores would is approximately (-5.6, -1.3).
Since 0 is apparently an unusual value for the statistic, then at the 5% significance level we would fail to reject
a null hypothesis of that claims that the fathers' and mothers' average IQs are equal.
Transcribed Image Text:4. Researchers studying IQ scores of mothers and fathers of `gifted" children collected data from 36 gifted children and their parents. First, differences in IQ scores of the father and the mother were calculated for each child (calculated as father's IQ score - mother's IQ score). The dot plot below shows the bootstrap distribution of means of 200 bootstrap samples taken from this original sample of differences in IQ scores. The mean of the bootstrap distribution is approximately -3.48 points and the bootstrap standard error is 1.3 points. Assume the usual conditions for constructing a bootstrap confidence interval are satisfied. Which of the following statements is false? -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 O A 95% bootstrap confidence interval for the difference in IQ scores is approximately (-6, -0.9). It's likely that in the original sample, most mothers had higher IQ scores than the fathers. A 90% bootstrap confidence interval for the difference in IQ scores would is approximately (-5.6, -1.3). Since 0 is apparently an unusual value for the statistic, then at the 5% significance level we would fail to reject a null hypothesis of that claims that the fathers' and mothers' average IQs are equal.
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