Question

A local politician claims that more than 65% of residents favor granting police additional powers to tap phones. A sample of 560 residents resulted in 392 that favor giving police additional powers to tap phones. Conduct a hypothesis test using a 5% significance level to see if there is enough evidence to support the politician’s claim

PLEASE I NEED COMPUTERIZED SOLUTION WHICH I CAN COPY EASILY

Answer 1

Null hypothesis:

H0 :- p=0.65

i.e.excatly 65% of residents favour granting police additional power to tap phone

Alternative hypothesis :

h1 : p>0.65

i.e. more than 65% of residents favour granting police additional power to tap phone

number of total residentss (n) = 560

number of resident who in favour (X) =392

proportion (p) = x / n = 392/560 = 0.7

$\alpha$(level of significance) = 5%

Test statistics:

$z =\frac{p-P}{PQ/n}$

where P=0.65 , Q=1-P =0.35

$z =\frac{0.7-0.65}{sqrt(0.65*0.35)/560}$

z= 2.48069

z at 5% is 1.645

since, z stat (2.48)> z tab (1.645) hence we reject null hypothesis at 5% level of significance.

Hence ,there is enough evidence to support the politician claim.