Question 1159397: A machine is supposed to mix peanuts, hazel-nuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans. At the 0.05 level of significance, test the hypothesis that the machine is mixing the nuts in the ratio 5:2:2:1
Answer by LChester89(3)   (Show Source):
You can put this solution on YOUR website! You can use a chi-square test of goodness of fit to solve this. The formula for finding the test statistic (x^2) is:  . O is the observed value (for example, 269 peanuts), and E is the expected value (ex: 250 peanuts). Though you can manually calculate chi-square, it would be much faster to use a chi-square goodness of fit calculator, which can be found at vassarstats.net under Frequency Data. After running a chi-square test, the test statistic for these data is 10.14, with 3 degrees of freedom. To find if this is statistically significant, you need to compare the test statistic (10.14) to the appropriate critical value for 3 degrees of freedom. You can find the chi-square critical values chart online. The critical value is 7.815. Because 10.14 is bigger than 7.815, your result is statistically significant, and you can reject your null hypothesis (meaning that this nut ratio inside the can does not fit the expected ratio of 5:2:2:1).
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