Question

14. A recent Gallop poll shows that Trump’s popularity as the presidential candidate is 40% based on 1,024 people. Conduct a hypothesis test for the unknown population proportion claiming that Trump’s popularity is definitely less than the current Biden’s 44%. Use p-value method at alpha = 0.05.

Answer 1

Solution;

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.44

Ha: p < 0.44

Test statistics

z = ( - ) / *(1-) / n

= ( 0.40 - 0.44) / (0.44*0.56) / 1024

= -2.579

P-value = P(Z < z )

= P(Z < -2.579)

= 0.0050

The p-value is p = 0.0050, and since p = 0.0050 < 0.05, it is concluded that the null hypothesis is rejected.

There is enough evidence to the unknown population proportion claiming that Trump’s popularity is definitely less than the current Biden’s 44%.