(Solved): A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can c ...

A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to have 273 peanuts, 119 hazelnuts, 80 cashews, and 28 pecans. At the \( 0.025 \) level of significance, test the hypothesis that the machine is mixing the nuts in the ratio \( 5: 2: 2: 1 \). Click here to view page 1 of the table of critical values of the chi-squared distribution. Click here to view page 2 of the table of critical values of the chi-squared distribution. State the hypotheses for the test. \( \mathrm{H}_{0} \) : The machine \( \quad \) nuts in the ratio \( 5: 2: 2: 1 \). \( \mathrm{H}_{1} \) : The machine \( \quad \) nuts in the ratio \( 5: 2: 2: 1 \). The test statistic is (Round to two decimal places as needed.) The critical region is \( \chi^{2}> \) (Round to two decimal places as needed.) State the conclusion. the null hypothesis. There sufficient evidence to conclude that the machine the nuts in the ratio \( 5: 2: 2: 1 \).