Question

in a study of cell phone usage and brain hemispheric dominance, an internet survey was e - mailed to 6980 subjects randomly selected from an online group involved with ears. there were 1312 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 > 0.2 )
c. ( h_0:p = 0.2 )
( h_1:p
eq0.2 )
d. ( h_0:p < 0.2 )
( h_1:p = 0.2 )
e. ( h_0:p
eq0.2 )
( h_1:p = 0.2 )
f. ( h_0:p = 0.2 )
( h_1:p < 0.2 )

the test statistic is ( z=-2.51 )
(round to two decimal places as needed.)

the p - value is 0.006
(round to three decimal places as needed.)

because the p - value is the significance level, the null hypothesis. there is evidence to support the claim that the return rate is less than 20%

Explanation:

Step1: Compare P - value and significance level

We are given a significance level of \( \alpha=0.01 \) and a P - value of \( P = 0.006 \).
Since \( P=0.006\) and \( \alpha = 0.01\), and \(0.006<0.01\) (i.e., \(P<\alpha\)).

Step2: Make a decision about the null hypothesis

When \(P <\alpha\), we reject the null hypothesis \(H_{0}\).

Step3: Draw a conclusion

Since we reject the null hypothesis \(H_{0}:p = 0.2\), there is sufficient evidence to support the claim that the return rate \(p\) is less than \(20\%\) (i.e., \(p<0.2\)).

Answer:

Because the P - value is less than the significance level, reject the null hypothesis. There is sufficient evidence to support the claim that the return rate is less than \(20\%\).