Stat 301 Day 10 Normal approximation to Binomial

Stat 301 – Day 10 Normal approximation to Binomial

Last Time Ho true Reject Ho Type I Error Type II Error Fail to reject Ho n n n Type I and Type II Errors Calculating Power Direction of alternative q Ho false Rejection region X > 9 P(Type I Error) < 0. 05 Including two-sided P(Type II error) Power = P(in rejection region) = P(X < 8 when p = 0. 333)

Future calculations (p. 60) n PP 1. 7 D

Investigation 1. 8 n n Skipping Key idea: Distribution of sample proportions rather than sample counts

Calculating the SD n

Normal approximation to binomial (aka Central Limit Theorem) n Will allow ourselves to use the normal distribution when np > 10 and n(1 -p) > 10

So then! n Can do cool things like predict 95% of sample proportions will fall within 2 SD of p. . .

Investigation 1. 9 (p. 67) n Work with partner (a)-(o)

Advantages to Normal Distribution n n Used to be more convenient for calculating probabilities (area under the curve) Can assume perfect symmetry in the distribution q q n e. g. , can assume roughly 95% of results fall within 2 standard deviations of the mean z=observation-mean std dev Can now more easily explain why there is more precision with larger samples

Project 1 n Project proposal q q q Find a group of 3 individuals Self sign-up as a project group Brainstorm topics Thursday we will talk about sampling Turn in project topic idea by Monday (at the latest, if sooner can start collecting data sooner)

To Do n n Finish Investigation 1. 9 through (o) and read Study Conclusions and Summary of One Proportion z-test Take Quiz 10