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$\backslash$table$[[$A$,$B$,$C$,$D$,$E$],[5,8,14,21,12]]$

Do the largest companies differ in performance from the performance of the $1,000$ companies in the Shareholder Scoreboard? Use $a=0\mathrm{.}05.$

State the null and alternative hypotheses.

$H_0$ : The proportions of the largest companies compared to the $1,000$ companies are the same for at least one of the five groups.

$H_a$ : The proportions of the largest companies compared to the $1,000$ companies are different for all five groups.

$H_0$ : The proportions of the largest companies compared to the $1,000$ companies are the same for the majority of the five groups.

$H_a$ : The proportions of the largest dampanies compared to the $1,000$ companies are different for the majority of the five groups.

$H_0$ : The largest companies do not differ in performance from the $1,000$ companies.

$H_a$ : The largest companies differ in performance from the $1,000$ companies.

$H_0$ : The largest companies differ in performance from the $1,000$ companies.

$H_a$ : The largest companies do not differ in performance from the $1,000$ companies.

Find the value of the test statistic. $($Round your answer to three decimal places.$)$

Find the $p-$value. $($Round your answer to four decimal places.$)$

$p-$value $=$

State your condusion.

Do not reject $H_0.$ We condude that the largest companies do not differ in performance from the $1,000$ companies.

Reject $H_0.$ We conclude that the proportions of the largest companies compared to the $1,000$ companies are different for all five groups.

Do not reject $H_0.$ We conclude that the proportions of the largest companies compared to the $1,000$ companies are the same for the majority of the five groups.

Reject $H_0.$ We conclude that the largest companies differ in performance from the $1,000$ companies.

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