Question

A U.S. government survey in 2007 said that the proportion of young Americans that earn a high school diploma is 0.87. a)Suppose you took a simple random sample of 100 young Americans. We know because of sampling variability that the sample proportion of those who earned a high school diploma would vary each time you took a sample. Assuming the value above can be taken as the population proportion (i.e. as a parameter), what model can be used to describe how these sample proportions would vary

Answer 1

normal distribution can be used to model the sample proportions

Explanation:

N ( sample size ) = 100

probability of earning high school diploma (p) = 0.87

probability of not earning high school diploma ( q ) = 0.13

hence ;

∈( P ) = p = 0.87

Var ( p ) =
`(pq)/(n)` =
`(0.86 * 0.13 )/(100)` = 0.001131

therefore ; p ~ N = ( 0.87 , 0.001131 )