SOLUTION: 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 269 peanuts, 112 hazelnuts

Question 1193955: 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 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans. At the 0.05
level of significance. Which test will be used to test the hypothesis that
the machine is mixing the nuts in the ratio 5:2:2:1. State the Null and
Alternative hypothesis.
Answer by parmen(42) (Show Source): You can put this solution on YOUR website!
**Test to be used:**
The appropriate test for this scenario is the **Chi-Square Goodness-of-Fit Test**. This test is used to determine if the observed frequencies of different categories in a sample significantly differ from the expected frequencies under a specific hypothesis.
**Null and Alternative Hypotheses:**
* **Null Hypothesis (H0):** The machine is mixing the nuts in the expected ratio of 5:2:2:1.
* **Alternative Hypothesis (H1):** The machine is not mixing the nuts in the expected ratio of 5:2:2:1.
**In essence:**
* The null hypothesis states that the observed frequencies of peanuts, hazelnuts, cashews, and pecans in the can are consistent with the expected ratio.
* The alternative hypothesis states that the observed frequencies are significantly different from the expected ratio, suggesting that the machine is not mixing the nuts correctly.

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