Question

10)

We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is 0.02.

H₀: 50% of community college students plan to vote in the next presidential election.

H_a: More than 50% of community college students plan to vote in the next presidential election.

What can we conclude?

Group of answer choices

Nothing. The sample size is too small to represent all community college students.

The evidence suggests that the majority of community colleges students plan to vote in the next presidential election because 54% is greater than 50%.

The evidence does not suggest that the majority of community colleges students plan to vote in the next presidential election because the difference between 50% and 54% is not statistically significant. A 4% difference could be due to random chance.

The evidence suggests that the majority of community colleges students plan to vote in the next presidential election because the P-value is less than the significance level.

Answer 1

We need to test the population proportion P for voting percentage.

We survey 650 randomly selected community college students and find that 54% of them plan to vote.

H₀: 50% of community college students plan to vote in the next presidential election.

H_a: More than 50% of community college students plan to vote in the next presidential election.

After conducting the test we get the P-value is 0.02.

also, we choose a significance level of 0.05.

since p-value < 0.05 we reject H0: and claim that the proportion is higher than 50%.

(The evidence suggests that the majority of community colleges students plan to vote in the next presidential election because the P-value is less than the significance level.)