Question

.In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.05 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions

Answer 1

Since the calculated value exceeds the critical value;

we Reject Null hypothesis.

We conclude that, there is no sufficient evidence that The percentage of people who believe they voted for winning candidate is equals to 43% or 0.43

Explanation:

Given the data in the question;

308 out of 611 voters are surveyed saying they voted for the candidate that won.

that is;

x = 308

sample size n = 611

Hypothesis;

Null hypothesis H₀ : p = 43% or 0.43 { The % of people who believe they voted for winning candidate equals 43% }

Alternative hypothesis H₁ : p ≠ 43% or 0.43 { The % of people who believe they voted for winning candidate is not equal to 43% }

Sample proportion p" = x / n = 308 / 611 = 0.504

level of significance ∝ = 0.05

Critical value of Z =
`Z_{\alpha /2` = 1.96

Test Statistics

z = (p" - p) / √( p(1-p) / n )

we substitute

z = (0.504 - 0.43) / √( 0.43(1-0.43) / 611 )

z = 0.074 / √( 0.2451 / 611 )

z = 0.074 / 0.02

z = 3.7

We compare;

Since the calculated value is exceeds the critical value;

we Reject Null hypothesis.

We conclude that, there is no sufficient evidence that The percentage of people who believe they voted for winning candidate is equals to 43% or 0.43