Question II. The following two-by-three table gives the sample proportions corresponding to different combinations of factor categories (for example, 28% of the sample fell in the cell representing category 1 of factor A and category 3 of factor B). A B .13 .19 .28 .07 .11 .22 II(a). Suppose that the sample size is n=100. Carry out a chi-squared test of independence at the 10% significance level. Make sure to state the null and alternative hypotheses, degrees of freedom, the value of your test statistic, the p-value, and the final conclusion. II(b). Now, suppose that n=1000 and repeat part 3(a). II(c). Find the smallest value of n that will result in rejection of the null hypothesis of part 3(a) at 10% level. Start by finding the appropriate x² statistic (which will depend on the n).

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**Question II.**

The following two-by-three table gives the sample proportions corresponding to different combinations of factor categories (for example, 28% of the sample fell in the cell representing category 1 of factor A and category 3 of factor B).

\[
\begin{array}{c|ccc}
 & \multicolumn{3}{c}{B} \\
A & 0.13 & 0.19 & 0.28 \\
 & 0.07 & 0.11 & 0.22 \\
\end{array}
\]

**II(a).** Suppose that the sample size is *n*=100. Carry out a chi-squared test of independence at the 10% significance level. Make sure to state the null and alternative hypotheses, degrees of freedom, the value of your test statistic, the p-value, and the final conclusion.

**II(b).** Now, suppose that *n*=1000 and repeat part 3(a).

**II(c).** Find the smallest value of *n* that will result in rejection of the null hypothesis of part 3(a) at the 10% level. Start by finding the appropriate χ² statistic (which will depend on the *n*).
Transcribed Image Text:**Question II.** The following two-by-three table gives the sample proportions corresponding to different combinations of factor categories (for example, 28% of the sample fell in the cell representing category 1 of factor A and category 3 of factor B). \[ \begin{array}{c|ccc} & \multicolumn{3}{c}{B} \\ A & 0.13 & 0.19 & 0.28 \\ & 0.07 & 0.11 & 0.22 \\ \end{array} \] **II(a).** Suppose that the sample size is *n*=100. Carry out a chi-squared test of independence at the 10% significance level. Make sure to state the null and alternative hypotheses, degrees of freedom, the value of your test statistic, the p-value, and the final conclusion. **II(b).** Now, suppose that *n*=1000 and repeat part 3(a). **II(c).** Find the smallest value of *n* that will result in rejection of the null hypothesis of part 3(a) at the 10% level. Start by finding the appropriate χ² statistic (which will depend on the *n*).
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