7.1-7.2 Classnotes-9

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Real life: We only get one chance In simulations we repeat the survey many times to understand, but in real life we just get one chance. Bias and precision are both measures of what happens if we could repeat the survey many times. Bias indicates the typical outcome of surveys repeated again and again. If the bias 1s 0, we will usually get the right value. If the bias is 0.10, then our estimate will characteristically be 10 percentage points too high. Precision measure how much our estimator will vary from the typical value if we do the survey again. If someone else does the survey how different will that person's estimate be from ours. If real life we don't know the true value of the population proportion, p. Which means we can not calculate the standard error. We can come close if we use the sample proportion, P . 1. AneNie Estimated standard error: est Book Problems: 23 (use the example we did in notes), 25,27,31 *7.25 Bias? Suppose that, when taking a random sample of 4 from 123 women, you get a mean height of only 60 inches (5 feet). The procedure may have been biased. What else could have caused this small mean? 7.27 Proportion of Odd Digits A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8). a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 55185 74834 81172 89281 48134 71185 b. Does the proportion found in part (a) represent p (the sample proportion) or p (the population proportion)? c. Find the error in this estimate, the difference between p and p (or p = p). ¢« 7.31 What Is the Proportion of Seniors? A population of a. Use the first line (reprinted here) from the random number table to select your sample of two. (The selections are underlined.) 02779 72645 32699 86009 Report the percentage of seniors in the sample. (Count the number of 4s and 5s and divide by the sample size 2.) b. Use the next line to select your sample of two. 31867 85872 91430 45554 Report the percentage of seniors in the sample. ¢. Use the next line to select your sample of two. 07033 75250 34546 75298 Report the percentage of seniors in the sample. d. Use the last line to select your sample of two. 09084 98948 09541 80623 Report the percentage of seniors in the sample. e. Fill in the rest of the table below, showing the results of the four samples: p (Population p (Sample Proportion of Proportion Repetition Senio i o B college students is taking an advanced math class. In the class 3 rs) of Seniors) Error: p p are three juniors and two seniors. Using numbers 1, 2, and 3 to 1 (from part a) 2/5=04 1/2=05 05-04=0.1 represent juniors and 4 and 5 to represent seniors, sample wn:.hout 5 replacement. Draw a sample of two people four times (once in each (from part b) 3 of parts a, b, ¢, and d), and then fill in the following table. 4
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