Question

A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1000 registered voters and found that 520 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate.
We test

H0:p=.50
Ha:p>.50

(a) What is the z-statistic for this test?  

(b) What is the P-value of the test?  

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p > 0.50

= x / n = 520 / 1000 = 0.520

1 - P₀ = 0.50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.520 - 0.50 / [(0.50 * 0.50) / 1000]

z = 1.265

P(z > 1.265) = 1 - P(z < 1.265) = 0.1029

P-value = 0.1029