Questions: A manufacturer of chocolate chips would like to know if its bag filling machine works correctly at the 438 gram setting. It is believed the machine is under filling the bags, thus cheating customers. Thirty seven bags were sampled and found to have a mean of 435 grams. Assume the population standard deviation is 14. Using a 0.05 significance level, determine if the bag filling machine is under filling the bags (that is, less than 438 grams).

A manufacturer of chocolate chips would like to know if its bag filling machine works correctly at the 438 gram setting. It is believed the machine is under filling the bags, thus cheating customers. Thirty seven bags were sampled and found to have a mean of 435 grams. Assume the population standard deviation is 14. Using a 0.05 significance level, determine if the bag filling machine is under filling the bags (that is, less than 438 grams).
Transcript text: A manufacturer of chocolate chips would like to know if its bag filling machine works correctly at the 438 gram setting. It is believed the machine is under filling the bags, thus cheating customers. Thirty seven bags were sampled and found to have a mean of 435 grams. Assume the population standard deviation is 14. Using a 0.05 significance level, determine if the bag filling machine is under filling the bags (that is, less than 438 grams).
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Solution

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Solution Steps

Step 1: State the null and alternative hypotheses
  • Null hypothesis (\(H_0\)): \(\mu = 438\)
  • Alternative hypothesis (\(H_a\)): H_a: \mu < \mu_0
Step 2: Calculate the test statistic
  • Test statistic (Z): -1.3
Step 3: Determine the critical value(s)
  • Critical value: -1.64
Step 4: Make a decision
  • Decision: do not reject \(H_0\)

Final Answer:

There is not sufficient evidence to reject the null hypothesis. This suggests the manufacturing process may be operating at the target mean.

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