A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 423 gram setting. it is believed that the machine is underfilling the bags. A 24 bag sample had a mean of 417 grams with a variance of 196 . A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
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\(\boxed{\text{Final Answer: The null hypothesis is that the machine is filling the bags correctly at 423 grams. The alternative hypothesis is that the machine is underfilling the bags.}}\)
Step 1 ：The manufacturer wants to test if the chocolate chip bag filling machine is working correctly at the 423 gram setting. It is suspected that the machine is underfilling the bags. A sample of 24 bags was taken and it was found that the mean weight of the bags was 417 grams with a variance of 196. A level of significance of 0.05 will be used for this test. It is assumed that the population distribution is approximately normal.
Step 2 ：The null hypothesis for this test is that the machine is filling the bags correctly at 423 grams. This is represented as \(H_0: \mu = 423\).
Step 3 ：The alternative hypothesis is that the machine is underfilling the bags. This is represented as \(H_1: \mu < 423\).
Step 4 ：\(\boxed{\text{Final Answer: The null hypothesis is that the machine is filling the bags correctly at 423 grams. The alternative hypothesis is that the machine is underfilling the bags.}}\)
