Research question: Do the majority of U. S. adults oppose the death penalty?

Based on this research question, here are the hypotheses:

LaTeX: H_0H 0: 50% of U. S. adults oppose the death penalty.

LaTeX: H_aH a: A majority (more than 50% of adults) oppose the death penalty.

Suppose a survey was conducted in which a random sample of 1,100 U. S. adults are asked about their opinions on the death penalty, and based on the data, the researchers state, "at the 5% significance level, this survey provides strong evidence that the majority of U. S. adults oppose the death penalty.

Which of the following P-values support this conclusion?

a. 0.55
b. 0.10
c. 0.03

The P-value that will support this conclusion is 0.03.

Step-by-step explanation:

We are given the following hypothesis below;

Null Hypothesis, : p = 50%    {means that 50% of U.S. adults oppose the death penalty}

Alternate Hypothesis, : p > 50%     {means that majority (more than 50% of adults) oppose the death penalty}

Now, a survey was conducted in which a random sample of 1,100 U.S. adults are asked about their opinions on the death penalty, and based on the data, the researchers state, "at the 5% significance level, this survey provides strong evidence that the majority of U.S. adults oppose the death penalty.

The above information concluded that the null hypothesis has been rejected due to which we moves towards the conclusion that majority of U.S. adults oppose the death penalty.

Now, the decision rule based on P-value criterion is given by;

Here, the P-value which will support our conclusion is 0.03 as at only this value our P-value is less than the level of significance of 0.05 and null hypothesis is rejected.