Question

identify the type i error and the type ii error that correspond to the given hypothesis. the percentage of households with internet access is less than 60%. access is equal to 60% when that percentage is actually less than 60%. identify the type ii error. choose the correct answer below. a. reject the null hypothesis that the percentage of households with internet access is equal to 60% when the percentage is actually equal to 60%. b. fail to reject the null hypothesis that the percentage of households with internet access is equal to 60% when that percentage is actually less than 60%. c. reject the null hypothesis that the percentage of households with internet access is less than 60% when that percentage is actually less than 60%. d. fail to reject the null hypothesis that the percentage of households with internet access is less than 60% when the percentage is actually equal to 60%.

Explanation:

• Type I error: Rejecting the null hypothesis when it is true.
• Type II error: Failing to reject the null hypothesis when it is false.
• The null hypothesis \(H_0:p = 0.6\) (where \(p\) is the proportion of households with Internet access), and the alternative hypothesis \(H_1:p<0.6\).
• For a Type II error, we fail to reject \(H_0\) when \(H_1\) is true. That is, we fail to reject the null hypothesis that the percentage of households with Internet access is equal to \(60\%\) when the actual percentage is less than \(60\%\).

Answer:

B. Fail to reject the null hypothesis that the percentage of households with Internet access is equal to \(60\%\) when that percentage is actually less than \(60\%\).