Ch. 20 Chance errors in sampling

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Ch. 20 Chance errors in sampling Finding the EV and SE of a percent Our temporary assumptions are that we know how to find the average & SD of a box.

Example 1: We have a group of 100,000 people, of which 20% have college degrees and 80% do not. Suppose we draw an SRS of 100 people. Fill in the blanks: The percent of college educated people in the sample is around ____, give or take ____ or so.

Set up the box model and determine how many tickets there are of each type. Find the average, SD of the box, EV of the sum, SE of the sum. Change to percents.

In general, EV of percent = x100% SE of percent = x100% A flaw in SRS is that it is not realistic. If the population size is large compared to the sample size, EV & SE are good approximations. (Correction for SE discussed later & EV doesn’t need to corrected. See Ex. A #4 solution)

EV for percentage for a sample is equal to population percentage. EV & SE for percentages depend on average and SD of box and sample size, not population size. EV for percentage for a sample is equal to population percentage. Increasing the sample size (# of draws) increases the EV of sum increases the SE of sum, but more slowly than EV. no effect on EV for percent SE for percent decreases

Example 2: Same situation as Example 1 except the sample size is 400. When we multiply the sample size by 4, the SE for the percentage is the original samples SE for %

Activity: Work in pairs on Exercise Set A #2, 6 p. 361 #2. A university has 25,000 students, of whom 10,000 are older than 25. The registrar draws an SRS of 400 students. a) Find the EV & SE for the number of students in the sample older than 25. b) Find the EV & SE for the percentage of students in the sample older than 25. c) The percentage of students in the sample who are older than 25 will be around ____ , give or take ______ or so.

#6. 900 draws are made at random with replacement from a box which has 1 red marble and 9 blue ones. The SE for the percentage of red marbles in the sample is 1%. A sample percentage which is 1 SE above its EV equals: _________ CHOICES: 10%+1% (2) 1.01x10% Explain.

Using the Normal Curve Example 3: Return to Example 1. Estimate the chance that more than 22% of the sample will have college degrees. Why is it okay to use the normal curve for estimates? We know that it is okay for sums and a percent is just a re-scaling of a sum.

In our college degree example, the variable was qualitative, so the variable was clear cut. Compare this to the example in the book on p. 363. Here the variable is quantitative and the cut-point is arbitrary. This could lead to potential interpretation issues and possibly biases results. Note: We do not yet have a way to work with average income in a sample, just net income.

Correction factor SE when drawing without replacement = (correction factor)x(SE when drawing with replacement) Correction factor =