9.4 ZTest of Hypothesis for the Proportion 311 378 orders were filled correctly.
ID: 3060491 • Letter: 9
Question
9.4 ZTest of Hypothesis for the Proportion 311 378 orders were filled correctly. At the 0.01 level of significance, can you conclude that the new process has increased the proportion of orders filled correctly? SOLUTION The null and alternative hypotheses are H0 : 0.909 (i.e., the population proportion of orders filled correctly using the new process is less than or equal to 0.909) , : > 0.909 (i.e., the population proportion of orders filled correctly using the new process is greater than 0.909) Since X = 378 and n-X = 22, both > 5, using Equation (9.3) on page 308, X 378 n 400 p =-= = 0.945 0.945-0.909 0.036 25034 T-)909-0909) 00144 400 The p-value (computed by Excel) for ZsTAT 2.5034 is 0.0062. Using the critical value approach, you reject Ho if ZSTAT 2.33. Using the p-value approach, you reject Ho if the p-valueExplanation / Answer
Solution 9.52:
Given,
Sample size = n = 400
Defective items = x = 88
Formula for sample proportion of defective items = p = x / n
Hence proportion = p = 88 / 400 = 0.22 = 22%
Done
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