Question

A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1400 registered voters and found that 720 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=0.50

H0:p=0.50

(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

Ha : p 0.50

n = 1400

x = 720

= x / n = 720 / 1400 = 0.51

P0 = 0.50

1 - P0 = 1 - 0.50 =0.50

a ) Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.51 - 0.50/ [0.50*050 / 1400]

= 0.748

Test statistic = z = 0.75

b ) P(z > 0.75 ) = 1 - P(z < 0.75 ) = 1 -0.7734

P-value = 2 * 0.2266 =0.4532