I'm taking an intro-level statistics course and am really confused on something probably basic.
>A sample of 20 students. 55% (11/20) eat breakfast.
>Another sample of 2,000 students. 55% (1,100/2,000) eat breakfast.
>Which is more convincing that a majority of all students eat breakfast, or are they equally convincing?
>Answer: The smaller sample is more convincing because it's not improbable that 11 in a sample of 20 eat breakfast. It's more improbable that as many as 1,100 out of 2,000 would eat breakfast.
Maybe I'm missing something but it doesn't make sense. Aren't they exact same thing? How is 11/20 probable but not 1100/2000?
>A sample of 20 students. 55% (11/20) eat breakfast.
>Another sample of 2,000 students. 55% (1,100/2,000) eat breakfast.
>Which is more convincing that a majority of all students eat breakfast, or are they equally convincing?
>Answer: The smaller sample is more convincing because it's not improbable that 11 in a sample of 20 eat breakfast. It's more improbable that as many as 1,100 out of 2,000 would eat breakfast.
Maybe I'm missing something but it doesn't make sense. Aren't they exact same thing? How is 11/20 probable but not 1100/2000?
