Asked by CHARLOTTE BOSCO on May 06, 2024
Verified
Of 346 items tested,12 are found to be defective.Construct a 98% confidence interval for the percentage of all such items that are defective.
A) (1.18%,5.76%)
B) (0.93%,6.00%)
C) (3.34%,3.59%)
D) (1.85%,5.09%)
E) (0.13%,6.80%)
Defective Items
Products that fail to meet quality standards.
- Formulate confidence intervals for means and proportions based on the provided data.
- Realize the importance of confidence intervals in tangible polling examples, research conditions, and choice-making.
Verified Answer
MS
MATURA SELVARAJAHMay 11, 2024
Final Answer :
A
Explanation :
The confidence interval for a proportion can be calculated using the formula: CI=p^±Zp^(1−p^)nCI = \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}CI=p^±Znp^(1−p^) where p^\hat{p}p^ is the sample proportion (12/346), nnn is the sample size (346), and ZZZ is the Z-score corresponding to the confidence level (for 98%, Z ≈ 2.33). Plugging in the values, we get the confidence interval as approximately (1.18%, 5.76%).
Learning Objectives
- Formulate confidence intervals for means and proportions based on the provided data.
- Realize the importance of confidence intervals in tangible polling examples, research conditions, and choice-making.
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