MATH SOLVE

4 months ago

Q:
# 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 testH0:p=.50Ha:p>.50(a) What is the z -statistic for this test?(b) What is the P-value of the test?

Accepted Solution

A:

Answer: a) 1.07, b) 0.1423Step-by-step explanation:Since we have given that n = 1400Number of voters vote for Republican candidates = 720So, [tex]\hat{p}=\dfrac{720}{1400}=0.514286[/tex]And hypothesis are :[tex]H_0:p=0.50\\\\H_a:p>0.50[/tex](a) What is the z -statistic for this test?
[tex]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[/tex](b) What is the P-value of the test?p-value = P(Z>Z(statistics))[tex]P(z>1.07)\\\\=0.1423[/tex]Hence, a) 1.07, b) 0.1423