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. Provide your answer below. p-value

Answer 1

Solution:

Given:

n = 500

x = 19

We have to use TI 83/84 plus calculator to test whether the candidates opponent's claim is true and less than 5.4% of the ballots were defective.

Use following steps:

Press STAT and select TESTS

Select 1-prop Z Test

TI-84 Plus Silver Edition TEXAS INSTRUMENTS EDIT_CALC TESTS 4-Test.... 2: T-Test. 3:2-SampZTest... 42-SampITest 981-PropZTest... $:2-Prop Test STAT PLOTF1 TBLSETE2 FORMAT EI CALC F4 TABLE F5 WINDOW ZOOM TRACE GRAPH 2ND MODE DEL ALPHA X.T.e,n ANGLE APPS STAT DAW PRGM MATH DISTR VARS CLEAR

Enter numbers:

TI-84 Plus Silver Edition TEXAS INSTRUMENTS 1-PropZTest PO:.054 X: 19 n: 500 Proppo KPO >Po Calculate Draw TABLE F5 STAT PLOTF1 TBLSETF2 FORMAT ES WINDOW 200M CALC F4 TRACE GRAPH 2ND LLIT MODE DEL ALPHA X.T.6.n STAT DISTE MATH ANGLEDD APPS PRGM VARS CLEAR SIN cos TAN

Click on Calculate and press Enter

TI-84 Plus Silver Edition TEXAS INSTRUMENTS Prop.654 1-PropZtest Z=-1.582933013 P=.0567183695 P=.038 n=500 STAT PLOTF1 TBLSETF2 FORMAT F3 CALC F4 WINDOW 200M TRACE TABLE F5 GRAPH 2ND MODE DEL ALPHA 000 X.T.6,n STAT TEST A MATH CLEAR APPS PRGM VARS

Thus p-value = 0.056718

p-value = 0.057