Rochelle was curious about the gender ratio in mechanical engineering versus chemical engineering in American universities. She obtained separate random samples of
\[30\] students from each field of study. She found that
\[5\] of the mechanical engineering students in her sample were female, and
\[10\] of the chemical engineering students in her sample were female. She plans to use these results to make a two-sample
\[z\] interval to estimate the difference between the proportion of females in each field of study.
Which conditions for constructing this type of interval did Rochelle's samples meet?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Both samples were randomly selected from their populations.
A
Both samples were randomly selected from their populations.
(Choice B) The counts of successes and failures are sufficiently large in each sample.
B
The counts of successes and failures are sufficiently large in each sample.
(Choice C) Individual observations in each sample can be considered independent, and the samples themselves are independent.
C
Individual observations in each sample can be considered independent, and the samples themselves are independent.