MATH 1F92 Lecture Notes - Lecture 1: Confidence Interval, Simple Random Sample, Upper And Lower Bounds

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1F92
• Professor: Prof.Christian Deangelis

Document Summary

From the previous lecture, we now have a way of estimating whereabouts the population proportion may lie. For a sample proportion to be normally distributed, 2 conditions must be met: But if we our esti(cid:373)ati(cid:374)g p a(cid:374)d do(cid:374)(cid:859)t k(cid:374)ow what it is, how ca(cid:374) we check co(cid:374)ditio(cid:374) #1: np(cid:4666)(cid:883) p(cid:4667)(cid:3410)(cid:883)(cid:882, n(cid:3409)(cid:882). (cid:882)(cid:887)n. We would now instead of using (cid:858)p(cid:859) for the conditions, we would have to use instead: (cid:4666)(cid:883) (cid:4667)(cid:3410)(cid:883)(cid:882) (cid:884)(cid:4667) (cid:3409)(cid:882). (cid:882)(cid:887) So, in the same sense, if we defined a (cid:4666)(cid:883) (cid:4667) (cid:883)(cid:882)(cid:882)% confidence interval for a population. Exact same conditions, except replacing p with p hat. confidence interval for (cid:859)p(cid:859) is given by the following quantities: Suppose that a simple random sample of size n is taken from a population. Constructing a (cid:4666)(cid:2778) (cid:4667)% (cid:2778)(cid:2777)(cid:2777)% confidence interval for a population or the data are the result of a randomized experiment. Note: the conditions must be met for us to be able to take a confidence interval.