chi-square

chi-square - Using Your TI-83/84 Calculator for Hypothesis...

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Using Your TI-83/84 Calculator for Hypothesis Testing: The Chi-Square Goodness-of-Fit Test Dr. Laura Schultz If births were uniformly distributed across the week, we would expect that about 1/7 of all births occur during each day of the week. How closely do the observed number of births fit this expected distribution? The chi-square goodness-of-fit test is used to determine whether an observed frequency distribution is significantly different from the expected distribution, or how “good” (sic) the two distributions fit each other. If we were only interested in one day of the week, we could conduct a 1-proportion z test. However, because we have seven hypothesized proportions, we need to conduct a test that considers all of them together and gives an overall indication of whether the observed distribution differs from the expected one. The chi-square goodness-of-fit test is just what we need. Let’s consider the frequency distribution of all 2003 New Jersey births by day of the week. If you have a TI-84 Plus calculator, there is a built-in chi-square goodness-of-fit (GOF) test. If not, you will need to follow a somewhat more complicated procedure. I will provide instructions for both calculator models; use whichever method applies to your calculator. χ 2 Goodness-of-Fit Test for the TI-83 Calculator 1. Start by clearing L 1 , L 2 , and L 3 . We will need all three lists in order to compute the χ 2 test statistic. 2. Enter the observed number of births for each day of the week into L 1 . (The general procedure is to put observed frequencies in L 1 .) 3. Now we need to compute the expected frequency for each day of the week. Because we are hypothesizing that births are uniformly distributed, we calculate the expected frequency as E = n / k , where n is the total number of trials (births, in this case) and k is the number of different categories (days of the week, in this case). For this example, E = 116823/7 = 16689. We will use this expected frequency for each day of the week. (If we had been hypothesizing unequal frequencies, you
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chi-square - Using Your TI-83/84 Calculator for Hypothesis...

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