Many people believe that criminals who plead guilty tend to get lighter sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sample data for defendants in burglary cases. All of the subjects had prior prison sentences. Use a $0\mathrm{.}05$ significance level to test the claim that the sentence $($sent to prison or not sent to prison$)$ is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea?

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Determine the null and alternative hypotheses.

A$.H_0$ : Pleading guilty reduces a defendant's chance of going to prison.

$H_1$ : Pleading guilty does not reduce a defendant's chance of going to prison.

B$.H_0$ : The sentence $($sent to prison or not sent to prison$)$ is not independent of the plea. $H_1$ : The sentence $($sent to prison or not sent to prison$)$ is independent of the plea.

C$.H_0$ : Pleading guilty does not reduce a defendant's chance of going to prison.

$H_1$ : Pleading guilty reduces a defendant's chance of going to prison.

D$.H_0$ : The sentence $($sent to prison or not sent to prison$)$ is independent of the plea. $H_1$ : The sentence $($sent to prison or not sent to prison$)$ is not independent of the plea.

Determine the test statistic.

Round to three decimal places as needed.$)$

Determine the P$-$value of the test statistic.

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$\backslash$table$[[,$Guilty Plea,Not Guilty Plea$],[$Sent to Prison,$395,59],[$Not Sent to Prison,$554,41]]$

Use a $0\mathrm{.}05$ significance level to test the claim that the sentence $($sent to prison or not sent to prison$)$ is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea?

A$.$ There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants.

B$.$ There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants.

C$.$ There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants.

D$.$ There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants.