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%.

A. Define population mean in the context of the problem and state the appropriate hypotheses.

B. State and verify the conditions for this hypothesis test for a mean.

I need help ASAP with Part A and B. Thank You.

Answer 1

A) Population mean, = mean length of spaghetti noodles for Delectable Delight is 252 mm

The null and alternative hypotheses

Note : The null hypothesis is the hypothesis of no difference , thus we state , alternative hypothesis is generally the research hypothesis , that is what we want to test : whether mean is less than 252 mm

B) Conditions for hypothesis test for mean

i) Sample should be collected through simple random sampling .

As the sample of 40 noodles are collected through random sampling , first condition is satisfied .

ii) The sampling distribution of sample mean should follow Normal or nearly normal .This is possible if parent population is normal or sample size is big (n>30)

As sample size is big, n= 40 , second condition is also satisfied .

Thus conditions for hypothesis test for mean is satisfied .