Question 2 of 8, Step 1 of 1
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 442 gram setting. Based on a 12 bag sample where the mean is 432 grams and the standard deviation is 21 , is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normat. Find the value of the test statistic. Round your answer to three decimal places.

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Step 1 ：The question is asking for the value of the test statistic in a hypothesis test. The null hypothesis in this case is that the mean weight of the bags is 442 grams, and the alternative hypothesis is that the mean weight is less than 442 grams.

Step 2 ：The test statistic for a hypothesis test about a population mean is a z-score, which is calculated as (sample mean - population mean) / (standard deviation / sqrt(sample size)).

Step 3 ：In this case, the sample mean is 432 grams, the population mean is 442 grams, the standard deviation is 21 grams, and the sample size is 12.

Step 4 ：The z-score is calculated as follows: \((432 - 442) / (21 / \sqrt{12}) = -1.649572197684645\)

Step 5 ：The z-score is negative, which indicates that the sample mean is less than the population mean. This is consistent with the alternative hypothesis that the bags are underfilled.

Step 6 ：Final Answer: The value of the test statistic is \(\boxed{-1.650}\).