Eleven percent of the products produced by an industrial process over the past
several months have failed to conform to specifications. The company modifies the
process in an attempt to reduce the rate of nonconformities. In a random sample of
300 items from a trial run, the modified process produces 30 nonconforming items.
Do these results provide evidence that the modification is effective in reducing the
rate of nonconformities? You may assume conditions for inference are satisfied.
Answer in the blanks to show the work associated with exploring this claim.
To explore the suspicion above, conduct a significance test using the hypotheses:
p = 0.11
p ___________ 0.11
Blank #1: Determine the correct alternative hypothesis by filling in the blank with <,
> or not equals.
Blank #2: Report the test statistic to two decimal places
Blank #3: Report the p-value to four decimal places
Blank #4: Give the test decision: (reject or do not reject) H0
Blank #5: Evidence ______________(favors or does not favor) that the modified
process has reduced the rate of nonconformities
Blank #6: How large a sample, n, would you need to estimate p with margin of error
0.03 with 95% confidence (use z = 1.96)? Use p* = 0.10, the sample proportion
given in the problem. Use rounding rules for sample size determinations in reporting
your answer.
Blank #7: After computing the sample size above with your initial desired
confidence level and margin of error, you've decided realistically that you cannot
afford the determined n. To decrease the calculated n, you could (increase or
decrease) the margin of error?