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=.50
Ha:p>.50

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

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

Answer 1

Answer: a) 1.07, b) 0.1423

Step-by-step explanation:

Since we have given that

n = 1400

Number of voters vote for Republican candidates = 720

So, $\hat{p}=\dfrac{720}{1400}=0.514286$

And hypothesis are :

$H_0:p=0.50\\\\H_a:p>0.50$

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

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.514286-0.50}{\sqrt{\dfrac{0.50\times 0.50}{1400}}}\\\\z=1.06609\approx 1.07$

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

p-value = P(Z>Z(statistics))

$P(z>1.07)\\\\=0.1423$

Hence, a) 1.07, b) 0.1423