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Fill out the following below: Parameter: The following data represent the age (in weeks) at which babies first crawl based on
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\\\textbf{\underline{Solution}:}\\\text{Given data,}\\x=(52,30,44,35,39,26,47,37,56,26,39,28) \\\text{Sample size: n =12} \\\textbf{Parameter:} \\\text{Sample mean:} \bar{x}=\frac{\sum_{i=1}^{n}x_i}{n}=\frac{52+30+...+28}{12}=\frac{459}{12}=38.25 \\\text{Sample standard deviation: s}=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}=\sqrt{\frac{(52-38.25)^2+(30-38.25)^2+...+(28-38.25)^2}{(12-1)}}\\=\sqrt{\frac{1100.25}{11}} \approx 10.0011 \\\text{For 95\% confidence interval,}\\\alpha=1-0.95=0.05\\\because t_{\alpha/2,n-1}=t_{0.025,11}=2.201 \\\textbf{Formula}: \\\bar{x}-t_{0.025,11}\frac{s}{\sqrt{n}},\bar{x}+t_{0.025,11}\frac{s}{\sqrt{n}}\Rightarrow (38.35-2.201\frac{10.0011}{\sqrt{12}},38.35+2.201\frac{10.0011}{\sqrt{12}})\Rightarrow(31.8955,44.6044)\approx(31.9,44.6) \\\textbf{Interval}:\\\text{The 95\% confidence interval for the mean age at which a baby first crawls is:} \textbf{(31.9,44.6)}

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