Q44 · Practice questionTechnology-activeComplex unfamiliar5 marks
QUESTION 44 (5 marks)
A manufacturer claims that the proportion of defective components is . In a random sample of 300 components, 34 are defective. Assuming the claim is correct, use a normal approximation to determine the probability of obtaining a sample proportion at least as large as the observed value. Comment on whether the result would be unusual at the 5% level.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
Probability . The result is unusual at the 5% level.
Worked solution
The observed proportion is . Under , . Thus , so . Since , such a result would be unusual if the claimed population proportion were correct.
Determines the observed sample proportion .
Determines the standard deviation of under .
Standardises the observed sample proportion.
Determines the upper-tail probability, approximately .
Correctly comments that the result is unusual at the 5% level.
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