Math  /  Data & Statistics

QuestionFirstborn \begin{tabular}{lllll} \hline 99 & 116 & 103 & 123 & 110 \\ 104 & 94 & 92 & 82 & 85 \\ \hline \end{tabular} \begin{tabular}{lllll} \hline \multicolumn{4}{c}{ Secondborn } \\ \hline 103 & 96 & 120 & 120 & 123 \\ 99 & 110 & 99 & 101 & 108 \\ \hline \end{tabular} Send data to Excel
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Part 1 of 2
Construct a 99.8\% confidence interval for the difference in mean IQ between firstborn and secondborn sons. Let μ1\mu_{1} denote the mean IQ of the firstborn sons. Use tables to find the critical value and round the answers to at least one decimal place.
A 99.8\% confidence interval for the difference in mean IQ between firstborn and secondborn sons is \square

Studdy Solution
Calculate the confidence interval for the difference in means.
CI=(xˉ1xˉ2)±t×SE CI = (\bar{x}_1 - \bar{x}_2) \pm t^* \times SE
CI=(100.8107.9)±3.922×5.2 CI = (100.8 - 107.9) \pm 3.922 \times 5.2
CI=7.1±20.38 CI = -7.1 \pm 20.38
CI=(27.48,13.28) CI = (-27.48, 13.28)
The 99.8% confidence interval for the difference in mean IQ between firstborn and secondborn sons is:
(27.5,13.3) \boxed{(-27.5, 13.3)}

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