University:
Montgomery College
Course:
MATH 117: Elements of Statistics
Academic year:

2020
Views:

35

Pages:

2
Author:

Kolten Khan

Chapter 8 – Confidence Intervals –One Population Section 8.3 - Estimating a Population Proportion Assumptions • The sample is a simple random sample • The conditions for a binomial distribution are satisfied by the sample. That is: there are a fixed number of trials, the trials are independent, there are two categories of outcomes, and the probabilities remain constant for each trial. A “trial” would be the examination of each sample element to see which of the two possibilities it is. • The normal distribution can be used to approximate the distribution of sample proportions because np > 5 and nq > 5 are both satisfied. (q = 1 – p) Procedure for Constructing a Confidence Interval for p 1) Verify that the assumptions are satisfied. 2) Find the critical value z c (from table 5). 3) Evaluate the margin of error E. E = zc p•q n 4) Find the interval and write it in one of the following forms pE; p−E p p+E; ( p − E, p + E ) Round-Off Rule for Confidence Interval Estimates of p 3 significant digits Using the TI-83 to Construct Confidence Intervals for p: STAT>>TESTS choose A:1-propZInt. Notice: x must be a whole number If you have to calculate it, round it to the nearest whole number SAMPLE SIZE FORMULAS (Look at the book and copy them here) Do one of the problems from the book about sample size. 5) In an October 2003 poll conducted by the Gallup Organization, 684 of 1006 randomly selected adults aged 18 years old or older stated they think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother. a) Obtain a point estimate for the proportion of adults aged 18 or older who think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother. b) Verify that the requirements for constructing a confidence interval about p-hat are satisfied. c) Construct a 98% confidence interval for the proportion of adults aged 18 or older who think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother. Interpret the interval. d) We are _____% confident that the true proportion of adults aged 18 or older who think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother is between _________% and __________% e) With ______% confidence we can say that ________% adults aged 18 or older think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother with a margin of error of ________% f) The statement “98% confident” means that, if 100 samples of size _____ were taken, about _____ of the intervals will contain the parameter p and about ____ will not. g) For ______% of intervals constructed with this method, the sample percentage would not differ from the actual population proportion by more than ______ g) How many more adults should be included in the sample to be 98% confident that a point estimate p-hat will be within 1% of p? Use a p-hat of 0.68. h) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 98% confident that the point estimate p-hat will be within a distance of 0.01 from p?