Answer
a. $H_{o}: p = 0.196$
$H_{1}: p > 0.196$
b. Type-I Error: Sample evidence leads the school nurse to believe that the percentage of 6- to 11-year-olds who are overweight is higher or lower than 19.6% in her school district. However, in fact the percentage is 19.6%.
c. Type-II Error: Sample evidence leads the school nurse to believe that the percentage of 6- to 11-year-olds who are overweight is equal to 19.6% in her school district. However, in fact the percentage is greater or lower than 19.6%.
Work Step by Step
a. Null hypothesis (the percentage of overweight kids is 19.6%):
$H_{o}: p = 0.196$
Alternative hypothesis (the percentage of overweight kids is not 19.6%):
$H_{1}: p \ne 0.196$
b. Type-I Error: Sample evidence leads the school nurse to believe that the percentage of 6- to 11-year-olds who are overweight is higher or lower than 19.6% in her school district. However, in fact the percentage is 19.6%. In other words, the school nurse has rejected the null hypothesis ($H_o$), but it in fact is true.
c. Type-II Error: Sample evidence leads the school nurse to believe that the percentage of 6- to 11-year-olds who are overweight is equal to 19.6% in her school district. However, in fact the percentage is greater or less than 19.6%. In other words, the school nurse has not rejected the null hypothesis ($H_o$), when in fact the alternative hypothesis ($H_1$) is true.
