Question

Statistics for Criminology and Criminal Justice

The probability of being acquitted in criminal court in Baltimore, Maryland, is .40. You take a random sample of the past 10 criminal cases where the defendant had a public defender and find that there were seven acquittals and three convictions. What is the probability of observing seven or more acquittals out of 10 cases if the true probability of an acquittal is .40? By using an alpha of .05, test the null hypothesis (that the probability of an acquittal is .40 for defendants with public defenders), against the alternative hypothesis that it is greater than .40.

Answer 1

(a)

Question:

What is the probability of observing seven or more acquittals out of 10 cases if the true probability of an acquittal is .40?

Answer:
Binomial Distribution

n = 10

p = 0.40

q = 1 - p = 0.60

P(X7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X=10)

So,

P(X7) = 0.0548

So,

Answer is:

0.0548

(b)

Question:

By using an alpha of .05, test the null hypothesis (that the probability of an acquittal is .40 for defendants with public defenders), against the alternative hypothesis that it is greater than .40.

H0: Null Hypothesis: P = =0.40 the probability of an acquittal is .40 for defendants with public defenders)

HA: Alternative Hypothesis: P > 0.40 (The probability of an acquittal is greater than .40 for defendants with public defenders)

n = 10

= 7/10 = 0.7

= 0.05

From Table, critical value of Z = 1.64

Test Statistic is given by:

Since calculated value of Z = 1.936 is greater than critical value of Z = 1.64, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the probability of an acquittal is greater than .40 for defendants with public defender