Question

The process that makes the spaghetti noodles for Delectable Delights is supposed to produce noodles with an average length of 252 mm.   Allison, the Quality Control Manager, is concerned that Machine #42 is not working properly and the noodles it produces are too short.  You are asked to take a random sample of 40 noodles from Machine #42 and perform a hypothesis test to determine if the noodles produced by the machine are, on average, less than 252 mm.  Use a significance level of 5%.

1. Define  in the context of the problem and state the appropriate hypotheses. (10 pts)

2. State and verify the conditions for this hypothesis test for a mean. (10 pts)

Answer 1

a)In the given context we need to check if there are any quality issues in the noodle production.

b)For the given testing we will be assuming the sample mean would follow a normal distribution and conduct a one sample t test.

At 5% significance level, tcritical=t(0.95,39dof)=1.685

If we have t*>1.685, we would conclude saying there are quality issues and the mean noodle lenth is greater than 252mm.

If we have t*<1.685, we can conclude that the machine is producing noodles of length 252mm on an average.