91Ó°ÊÓ

A die was tossed 120 times and the results are listed below. \begin{tabular}{|c|c|c|c|c|c|c|} \hline Upturned face & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Frequency & 18 & 23 & 16 & 21 & 18 & 24 \\ \hline \end{tabular} Compute the \(\mathrm{X}^{2}\) statistic for this 1 by 6 contingency table under the hypothesis that the die was fair.

Is there a significant relationship between the hair color of a husband and wife? A researcher observes 500 pairs and collects the following data. \begin{tabular}{|c|c|c|c|c|c|} \hline \multirow{2}{*} { WIFE } & \multicolumn{4}{|c|} { H U S B A N D } & Row \\\ \cline { 2 - 5 } & Red & Blonde & Black & Brown & Total \\ \hline Red & 10 & 10 & 10 & 20 & 50 \\ \hline Blonde & 10 & 40 & 50 & 50 & 150 \\ \hline Black & 13 & 25 & 60 & 52 & 150 \\ \hline Brown & 17 & 25 & 30 & 78 & 150 \\ \hline Column total & 50 & 100 & 150 & 200 & 500 \\ \hline \end{tabular} The researcher wishes to test the theory that people tend to select mates with the same hair color. Test this theory at the level of significance \(\alpha=.01\).

Suppose that a sales region has been divided into five territories, each of which was judged to have an equal sales potential. The actual sales volume for several sampled days is indicated below. \begin{tabular}{|c|c|c|c|c|c|} \hline & \multicolumn{5}{|c|} { T e r r i t o r y } \\ \hline & A & B & C & D & E \\ \hline Actual Sales & 110 & 130 & 70 & 90 & 100 \\ \hline \end{tabular} What are the expected sales for each area? How many degrees of freedom does the chi-square statistic have? Compute \(\mathrm{X}^{2}\) and use the table of \(\mathrm{X}^{2}\) values to test the significance of the difference between the observed and expected levels of sales.

Experience in a certain apple-growing region indicates that about 20 per cent of the total apple crop is classified in the best grade, about 40 per cent in the next highest rating, about 30 per cent in the next highest rating, and the remaining 10 per cent in the fourth and lowest rating. A random sample of 50 trees in a certain orchard yielded 600 bushels of apples, classified as follows: 150 bushels of the highest quality apples 290 bushels of the next highest, 140 bushels of the next highest, and 20 bushels of the lowest quality apples Can we conclude that the applet in this orchard are typical?