Question

A candidate in an election lost by 5.4% of the vote. The candidate sued the state and said that more than 5.4% of the ballots were defective and not counted by the voting machine, so a full recount would need to be done. His opponent wanted to ask for the case to be dismissed, so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 19 defective ballots. Use a TI-83, TI-83 plus, or TI-84 calculator to test whether the candidate's opponent's claim is true and less than 5.4% of the ballots were defective. Identify the p-value, rounding to three decimal places

Answer 1

Answer: p value = 0.057

The candidate's opponent's claim of ( p < 0.054 ) is false

as p (0.057) is greater than 0.054.

(P > 0.054)

Explanation:

p₀ = 5.4% = 0.054

Claim: p < 0.054

n = 500

x = 19

To perform z test for the proportion, we use TI-83, TI-83 plus, or TI-84 calculator

first;

Press STAT and go to TESTS menu.

Go to 1-Prop Z TEST

p₀ : 0.054

x : 19

n : 500

Prop < p₀

Calculate.

Output:

z = -1.582933013

p = 0.0567183695

therefore

p value = 0.057 ( three decimal place)

there the candidate's opponent's claim of ( p < 0.054 ) is false

as p > 0.054