Question

in a study of cell phone usage and brain hemispheric dominance, an internet survey was e - mailed to 6970 subjects randomly selected from an online group involved with ears. there were 1331 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. ( h_0:p
eq0.2 ) ( h_1:p = 0.2 )
○ b. ( h_0:p>0.2 ) ( h_1:p = 0.2 )
○ c. ( h_0:p = 0.2 ) ( h_1:p>0.2 )
○ d. ( h_0:p = 0.2 ) ( h_1:p<0.2 )
○ e. ( h_0:p = 0.2 ) ( h_1:p
eq0.2 )
○ f. ( h_0:p<0.2 ) ( h_1:p = 0.2 )

Explanation:

The null hypothesis \(H_0\) is a statement of equality. The claim is that the return rate \(p\) is less than \(20\% = 0.2\). The null hypothesis for a proportion test is \(H_0:p = p_0\) (where \(p_0=0.2\) here), and the alternative hypothesis \(H_1\) is the claim. Since the claim is \(p<0.2\), we set \(H_0:p = 0.2\) and \(H_1:p<0.2\).

Answer:

D. \(H_0:p = 0.2\), \(H_1:p<0.2\)