Math  /  Data & Statistics

QuestionA firm sent out a random sample of 500 shipments in a new type of heavy-duty packaging. Eighteen of them damaged upon arrival at their destinations. Is it appropriate to use the methods of this section to construct a confidence interval for the proportion of shipments in heavy-duty packaging that are damaged upon arrival? If not, explain why not. Yes No, because a sample of size 500 is not large enough. No, because either np^n \hat{p} or n(1p^)n(1-\hat{p}) is less than 10 .

Studdy Solution
Determine if both np^ n \hat{p} and n(1p^) n(1-\hat{p}) are greater than or equal to 10:
- np^=1810 n \hat{p} = 18 \geq 10 - n(1p^)=48210 n(1-\hat{p}) = 482 \geq 10
Both conditions are satisfied.
Since both conditions are satisfied, it is appropriate to use the methods of this section to construct a confidence interval for the proportion of shipments in heavy-duty packaging that are damaged upon arrival.
Yes

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