4) The Bradfield Container Company makes \"cardboard\" boxes for commercial use

Question

4) The Bradfield Container Company makes "cardboard" boxes for commercial use (i.e., pizza boxes). One of the big issues for the company is the set-up time required to change over from one order to the next. At one particular machine, the set-up time is thought to be uniformly distributed between 10 and 21 minutes. To test whether this is true or not, a random sample of 180 set-ups on this machine was selected with set-up time rounded to the nearest two-minute intervals. The following results occurred: Set-up Time Frequency 10-11 minutes 13 12-13 minutes 23 14-15 minutes 40 16-17 minutes 44 18-19 minutes 40 20-21 minutes 20 a. What are the appropriate null and alternative hypothesis to be tested? b. Based on the null and alternative hypotheses stated in part a, determine the expected frequencies for each set-up time category C. Compute the test statistic and carry out the hypothesis test. (15 marks)

Explanation / Answer

Qeuestion2 .

H0 : The set up time follows Uniform distribution.

Ha : The setup time doesn't follow uniform distribution.

(b) Here as the data is unifrom distribution. than each setup time is equally probable. So, expected frequency for each class shall be 180/6 = 30

(c) The Observed- Expected Chi square table.

Here X2 = 27.8

and for alpha = 0.05 and dF = 6-1 = 5

p - value = Pr(X2 > 27.8) = 4 x 10-5 < 0.05

so we shall reject the null hypothesis and can say that setup time is not uniformly distributed.

Question 3.

Here Critical q = 3.38

We will use tukey post hoc test to compare the three means.

there are 3 pairs of means here.

for City 1 and CIty 2 :

Q1-2 = l(M1 - M2 )l/ sqrt [MSW  /n]

Where M1 , M2 are means of two groups

MSw = Mean square error for Within treatments

n = Number of treatments per sample.

Q1-2 = l (236. 2393 - 344.0701) l / sqrt [2583.949 /30]

Q1-2 = 107.8308/ 9.2807 = 11.6188

Now for city 1 and city 3

Q1-3 = l(M1 - M3 )l/ sqrt [MSW  /n]

Q1-3 = l (236.2393 - 201.5034) l / sqrt [2583.949 /30]

Q1-3 = 34.7359/ 9.2807 = 3.743

Now for city 2 and city 3

Q2-3 = l(M2 - M3 )l/ sqrt [MSW  /n]

Q2-3 = l (344.0701- 201.5034) l / sqrt [2583.949 /30]

Q1-3 = 142.5667/ 9.2807 = 15.3616

Here we can see that all Q values (Bold values) are greater than the critical value Q = 3.38 so we shall that all mean pairs are different from each other.

Set-up time Observed Frequency (o) Expected frequency (E) (O-E)^2/E 10-11 13 30 9.633 12-13 23 30 1.633 14-15 40 30 3.333 16-17 44 30 6.533 18-19 40 30 3.333 20-21 20 30 3.333 Sum 180 180 27.8

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