A large manufacturing company investigated the service it has received from supp

Question

A large manufacturing company investigated the service it has received from suppliers and discovered that, in the past, 32% of all materials shipments have been received late. However, the company recently installed a new system in which the suppliers are more closely linked to the manufacturing process. A random sample of 118 deliveries since the system was installed revealed that 22 deliveries were late. Use this sample information and 0.05 level of significance to test whether the proportion of late deliveries has been reduced significantly. Clearly formulate and describe the hypotheses using nontechnical language, show your work including any equation(s) used, and finally provide a conclusion in a non-technical language.

Explanation / Answer

from question given that x = 22 n =118 mean =0.32

Null Hypothesis (Ho): p 0.32

Alternative Hypothesis (Ha): p < 0.32

Sample proportion, p’ = X/n = 22/118 = 0.1864

Test Statistics Z = (p’ – p)/ p (1 – p)/n

Z = (0.1864 – 0.32)/0.32*0.68/118 = -3.11

Using Z-tables, the p-value is P [Z < -3.11] = 0.0009

Since p-value is less than 0.05 level of signiFcance, we reject the null hypothesis

. Hence, we can conclude that proportion of late deliveries was reduced significantly

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