Problem
Part 1 of 4 Points: 0.17 of 1 Save In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6964 subjects randomly selected from an online group involved with ears. There were 1296 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than $20 \%$. Use the P-value method and use the normal distribution as an approximation to the binomial distribution. Identify the null hypothesis and alternative hypothesis. A. \[ \begin{array}{l} H_{0}: p<0.2 \\ H_{1}: p=0.2 \end{array} \] c. \[ \begin{array}{l} H_{0}: p=0.2 \\ H_{1}: p>0.2 \end{array} \] E. $H_{0}: p>0.2$ \[ H_{1}: p=0.2 \] B. \[ \begin{array}{l} H_{0}: p \neq 0.2 \\ H_{1}: p=0.2 \end{array} \] D. \[ \begin{array}{l} H_{0}: p=0.2 \\ H_{1}: p \neq 0.2 \end{array} \] F. \[ \begin{array}{l} H_{0}: p=0.2 \\ H_{1}: p<0.2 \end{array} \]
Solution
Step 1 ：Identify the null hypothesis and alternative hypothesis.
Step 2 ：The null hypothesis is usually a statement of no effect or no difference. It is the hypothesis that the researcher is trying to disprove. In this case, the null hypothesis would be that the return rate is equal to 20%.
Step 3 ：The alternative hypothesis is what you might believe to be true or hope to prove true. In this case, the alternative hypothesis is that the return rate is less than 20%.
Step 4 ：Therefore, the correct hypotheses are: \(H_{0}: p=0.2\) and \(H_{1}: p<0.2\).
Step 5 ：Final Answer: \(\boxed{H_{0}: p=0.2, H_{1}: p<0.2}\)
