Question

It is alleged that there is discrimination against blacks in grand jury selection. Some survey suggested that 24% of those eligible for grand jury service were black. However inspecting a random sample of 1100 called to appear for possible jury duty, we found only 229 were blacks. Suppose we want to test the survey's claim against the alternative that the actual proportion of blacks called for jury duty is less than what the survey suggests.

1.Rejection region: We reject H₀ at 1% level of significance if: ( b is not correct )
a)z > 2.326.
b) |z| > 2.576.
c) z < −2.326.
d) None of the above.

2. The value of the test-statistic is: Answer to 3 decimal places.(-2.329 was not correct)

3. The p-value of the test is equal to: Answer to 4 decimal places. (0.0099 was not correct)

Answer 1

H0: p = 0.24

Ha: p < 0.24

a)

For left tailed test,

Z critical value at 0.01 significance level = -2.326

Rejection rule = Reject H0 if z < -2.326

b)

Sample proportion = 229 / 1100 = 0.2082

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.2082 - 0.24) / sqrt ( 0.24 ( 1 - 0.24) / 1100 ]

= -2.470

c)

p-value = P(Z < z)

= P(Z < -2.470)

= 0.0068

Since p-value < 0.01 significance level, Reject H0.