You are in charge of quality control at the Utica Ketchup Bottling plant. Your b

Question

You are in charge of quality control at the Utica Ketchup Bottling plant. Your bottles are labeled 14 ounces but due to natural imperfections in the bottling process, not every bottle contains precisely the same amount of ketchup. Let's assume that the volumes are distributed Normally with a standard deviation of 0.1 oz. Before a shipment of ketchup goes out the door, you take a random sample of 30 bottles and measure the volume of each. Before you approve a shipment, you must be convinced that the mean volume of the shipment exceeds 14 ounces with a significance level of alpha = 5%. Your random sample of 30 ketchup bottles has average volume x = 14.035 oz. (Please only answer one part at a time to give other students a chance to answer as well! Start with the first one!) Carefully state the null and alternative hypotheses for this scenario. Is this a one-sided or two-sided test? If you want to show that the average volume is at least 14 ounces and the average volume of your sample is 14.035 ounces, why can you not immediately approve the shipment base on the fact that 14.035 > 14 with no further testing? Calculate the p-value for this test. As the quality control manager, do you approve this batch of ketchup bottles for shipment ? Why or why not?

Explanation / Answer

The statistical software output for this problem is:

One sample Z hypothesis test:
: Mean of population
H0 : = 14
HA : > 14
Standard deviation = 0.1

Hypothesis test results:

4) p - value = 0.0276 < alpha (=0.05), So we will reject the null hypothesis.

Hence,

We have enough evidence to support the statement that mean volume of shipment exceeds 14 ounces. Therefore, i would approve the shipment as a quality control manager because it meets the desired specifications.

Mean n Sample Mean Std. Err. Z-Stat P-value 30 14.035 0.018257419 1.917029 0.0276

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