Exercises 1–6: standard deviation for proportions
in the previous lesson, you used simulated sampling distributions to learn about sampling variability in the sample proportion and the margin of error when using a random sample to
estimate a population proportion. however, finding a margin of error using simulation can be cumbersome and take a long time for each situation. fortunately, given the consistent
behavior of the sampling distribution of the sample proportion for random samples, statisticians have developed a formula that will allow you to find the margin of error quickly and
without simulation.
1. 30% of students participating in sports at union high school are female (a proportion of 0.30).
a. if you took many random samples of 50 students who play sports and made a dot plot of the proportion of female students in each sample, where do you think this distribution
will be centered? explain your thinking.
b. in general, for any sample size, where do you think the center of a simulated distribution of the sample proportion of female students in sports at union high school will be?