Answer to Question #317066 in Statistics and Probability for Ella

Question

a survey company, sws, claims that a majority of gen z voters prefer leni robredo as the next president over that of its main competitor, bongbong marcos. to test this claim 500 randomly selected people were surveyed. among them, 270 leni, 211 bbm, and 1919 could not make up their minds. determine whether there is sufficient evidence, at the 5% level of significance, to support the sws survey claim against the default that the population is evenly split in its preference. Show your calculations.

Answer 1

$H_0:\mu \leqslant 0.5\\H_1:\mu >0.5\\T=\sqrt{n}\frac{\hat{p}-0.5}{\sqrt{\hat{p}\left( 1-\hat{p} \right)}}=\sqrt{500}\frac{\frac{270}{500}-0.5}{\sqrt{\frac{270}{500}\left( 1-\frac{270}{500} \right)}}=1.79461\sim t_{n-1}=t_{499}\\P\left( T>1.79461 \right) =F_{t,499}\left( -1.79461 \right) =0.0367$

Since P-value is less than 0.05, the the sws survey claim is supported.