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ST 361: Ch 7.3 Estimation --- Interval Estimation for population proportion ---------------------------------------------------------------------------------------------------------------------Statistical inference for (population proportion) Background information (review) The natural statistic for estimating is ____________________________ If n is large (i.e., n 5 and n 1 5 ), the sampling distribution of p is Because is not known, so p is not known. Thus p is used in the formula to calculate p . However, unlike before where we have to find the critical value from a t -distribution, here we still use a Z-distribution, but this time it requires a more stringent criterion for “large n”, that is Confidence interval for : (Assume ______________________ ) The Confidence interval for is 1 Ex. Suppose that the proportion of the left-handed students at a certain university is . A random sample of 200 students was collected and found that 40 out of the 200 students are left-handed. (a) Use an unbiased estimator to compute a point estimate of . (b) What is the distribution of your estimator in (a)? Why? (c) What is the standard error of your estimator? (d) Your estimator in (a) is unbiased because (circle one) (3 points) i. Its distribution is normal ii. Its mean is equal to iii. Its SE is equal to 1 n iv. It is based on a sample with size greater than 30 (e) Construct and interpret the 95% confidence interval for . 2