Questions: Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below. Assume that both samples are Independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150. n 131.92 mm 5.15 mm 4000 B.C. 30 A.D. 150 30 136.88 mm 5.39 mm What are the null and alternative hypotheses? A. H0: σ1^2=σ2^2 B. H0: σ1^2=σ2^2 H1: σ1^2<σ2^2 H1: σ1^2 ≠ σ2^2 C. H0: σ1^2 ≠ σ2^2 D. H0: σ1^2=σ2^2 H1: σ1^2=σ2^2 H1: σ1^2 ≥ σ2^2 Identify the test statistic. F= (Round to two decimal places as needed.)
Transcript text: Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below. Assume that both samples are Independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150.
\begin{tabular}{rccc}
& $\mathbf{n}$ & $\bar{x}$ & $\mathbf{s}$ \\
4000 B.C. & 30 & 131.92 mm & 5.15 mm \\
A.D. 150 & 30 & 136.88 mm & 5.39 mm
\end{tabular}
What are the null and alternative hypotheses?
A. $H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2}$ B. $H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2}$
\[
H_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \quad H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2}
\]
C. $H_{0}: \sigma_{1}^{2} \neq \sigma_{2}^{2}$ D. $H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2}$
\[
H_{1}: \sigma_{1}^{2}=\sigma_{2}^{2}
\]
$H_{1}: \sigma_{1}^{2} \geq \sigma_{2}^{2}$
Identify the test statistic.
$\mathrm{F}=$ $\square$ (Round to two decimal places as needed.)
Solution
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