Question

in a study of cell phone usage and brain hemispheric dominance, an internet survey was e-mailed to 6055 subjects randomly selected from an online group involved with ears. there were 1335 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 < 0.2 )
( h_1:p = 0.2 )

○b. ( h_0:p = 0.2 )
( h_1:p
eq0.2 )

○c. ( h_0:p
eq0.2 )
( 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 > 0.2 )

○f. ( h_0:p > 0.2 )
( h_1:p = 0.2 )

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of no effect or no difference. Here, we are testing a claim about a proportion. The claim is that the return rate \(p\) is less than \(20\%\) (or \(p = 0.2\)). The null hypothesis for a proportion test is always an equality (it assumes the status - quo value). The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for. Since the claim is \(p<0.2\), the null hypothesis \(H_0:p = 0.2\) and the alternative hypothesis \(H_1:p<0.2\).

Answer:

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