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An agricultural grain company processes and packages various grains purchased from farmers. A high-volume conveyor line contains four chutes at the end, each of which is designed to receive and dispense equal proportions of grain into bags. Each bag is then stamped with a date code and the number of the chute from which it came. If the chute output proportions are not relatively equal, then a bottleneck effect is created upstream and the conveyor cannot function at peak output. Recently, a series of repairs and modifications have led management to question whether the grains still are being equally distributed among the chutes. Packaging records from 800 bags yesterday indicate that 220 bags came from Chute 1, 188 bags from Chute 2,218 bags from Chute 3 , and 174 bags from Chute 4.

a. State the null and altemative hypotheses to test if the proportion of bags filled by any of the chutes is different from $0.25$.

b. Calculate the value of the test statistic and the p-value.

c. What is your conclusion at the $10 \%$ significance level? Would your conclusion change at the $5 \%$ significance level?

Solution

VerifiedThis task requires formulating the competing hypotheses for a multinomial experiment.

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