Question

in a study of cell phone usage and brain hemispheric dominance, an internet survey was e-mailed to 5000 subjects randomly selected from an online group involved with ears. there were 1138 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.

h₀: p = 0.2
h₁: p < 0.2

the test statistic is z = - 1.88
(round to two decimal places as needed.)

the p - value is 0.032
(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 \(\alpha = 0.01\) and a P - value \(P=0.012\).

Step2: Make a decision about the null hypothesis

Since \(P = 0.012>0.01=\alpha\), we fail to reject the null hypothesis.

Answer:

Because the P - value is greater than the significance level, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the return rate is less than \(20\%\).