00:01
So our question says education and public health professionals are interested in how many adolescents between 15 and 18 years of age in youth detention facility have reading disability.
00:13
A comprehensive screening program found out that 38 adolescents were found to have reading disability and 369 adolescents did not have reading disabilities.
00:25
So the u .s.
00:26
Department of education estimates that about 9 % of adolescents in this age group have, reading disability we're supposed to conduct a hypothesis test to determine if there's a significant evidence to suggest that the population of the adolescents in youth detention facility has a reading disability prevalence that is different from 9 percent use a 5 percent level of significance so the first question is what is the z test so we have answers to pick from so let's try to extract out the needed parameters so 38 adolescents have reading disabilities so 38 adolescents have reading disability and 369 that's 369 does not have reading disability so that is no reading disability so that means a total number of adolescents that was mentioned that was tested right at 38 plus 369 and that gives us 4007 so we have a total of 407 adolescents.
01:37
According to the question, the u .s.
01:40
Department of education estimates that about 9 % of adolescents in the age group have a reading disability.
01:45
So that means our population proportion p is 9%, which is 0 .09.
01:51
So the sample proportion, so which is the fraction of adolescents that have reading disability from a total of 407 is going to be 38 divided by 407 and that 0 .093.
02:05
If you do, if you try 38 by 407, we have 0 .0933.
02:12
Exactly...