Question

A manufacturer wants to decrease the lead-time of cake box mixes. Past records indicate that the average lead-time of the mix is 214.55 days. After a revised operational process has been developed, a sample of 25 boxes of cake mix had a mean of 213.333 and a standard deviation of 1.005.

a. Using a 0.01 significance level, decide if the sample data support the claim that lead-time has decreased using a hypothesis test, five-steps

Answer 1

Data: n=25

  

s=1.005

We want to test the claim that lead time of cake box mixes has decreased.

The hypothesis testing problem is:

Vs

Here we have to assume the normality.

The test statistic is:

t critical value at 1% level of significance with 24 degrees of freedom for one tail test is

tcrit=-2.492 ### By using table

Since -6.05<-2.492, we reject the null hypothesis at 1% level of significance.

Therefore we have sufficient evidence to support the manufacturers claim that lead time of cake box mixes has decreased.