(Solution) - Packages of mixed nuts made by a certain company contain -(2025 Original AI-Free Solution)

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Packages of mixed nuts made by a certain company contain four types of nuts. The percentages of nuts of Types 1, 2, 3, and 4 are supposed to be 40%, 30%, 20%, and 10%, respectively. A random sample of nuts is selected, and each one is categorized by type.
a. If the sample size is 200 and the resulting test statistic value is X2 5 19.0, what conclusion would be appropriate for a significance level of .001?
b. If the random sample had consisted of only 40 nuts, would you use the chi-square test here? Explain your reasoning.