A large manufacturing company investigated the service it received from supplier

Question

A large manufacturing company investigated the service it received from suppliers and discovered that in the past, 32% of all materials shipments were received late. However, the company recently installed a just-in-time system in which suppliers are linked more closely to the manufacturing process. A random sample of 110 deliveries since the just-in-time system was installed reveals 20 deliveries were late. Using 5% level of significance, can you conclude that the system has significantly reduced late deliveries?

Explanation / Answer

Solution:

Null Hypothesis (Ho): p 0.32
Alternative Hypothesis (Ha): p < 0.32
Sample proportion, p’ = X/n = 22/110 = 0.2
Test Statistics
Z = (p’ – p)/ p (1 – p)/n
Z = (0.2 – 0.32)/0.32*0.68/110
Z = -2.69
Using Z-tables, the p-value is
P [Z < -2.69] = 0.0036
Since p-value is less than 0.05 level of significance, we reject the null hypothesis.Hence, we can conclude that proportion of late deliveries was reduced significantly.

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