Question

Judging on the basis of​ experience, a politician claims that 57​% of voters in a certain area have voted for an independent candidate in past elections. Suppose you surveyed 25 randomly selected people in that​ area, and 18 of them reported having voted for an independent candidate. The null hypothesis is that the overall proportion of voters in the area that have voted for an independent candidate is 57​%. What value of the test statistic should you​ report?

Answer 1

Answer: z= 1.51

Step-by-step explanation:

Test statistic for proportion is given by :-

$z=\dfrac{p-P}{\sqrt{\dfrac{PQ}{n}}}$

Where n is sample size ,p is the sample proportion , P Is the population proportion and Q =1 - P.

Given : P=57% = 0.57

Q= 1- P = 1-0.57=0.43

n = 25

$p=\dfrac{18}{25}=0.72$

Test statistic for proportion will be :-

$z=\dfrac{0.72-0.57}{\sqrt{\dfrac{0.57\times0.43}{25}}}\approx1.51$

We should report the value of test statistic z= 1.51