Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-Of 346 items tested, 12 are found to be defective. Construct the 98% confidence interval for the proportion of all such items that are defective.
A) 0.0110

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-Of 346 items tested, 12 are found to be defective. Construct the 98% confidence interval for the proportion of all such items that are defective.
A) 0.0110 < p < 0.0584
B) 0.0345 < p < 0.0349
C) 0.0118 < p < 0.0576
D) 0.0154 < p < 0.0540

Quizplus · Accepted Answer

We can calculate the sample proportion as:
p̂ = 12/346 = 0.0347
The margin of error (E) can be calculated as:
E = z*sqrt((p̂(1-p̂))/n), where n is the sample size and z is the z-score corresponding to the desired confidence level (98%). Using a calculator or a table, we find that z = 2.33.
Substituting the values, we get:
E = 2.33*sqrt((0.0347*0.9653)/346) ≈ 0.023
Finally, we can construct the confidence interval as:
p̂ - E < p < p̂ + E
0.0347 - 0.023 < p < 0.0347 + 0.023
0.0117 < p < 0.0577
Rounding to four decimal places, we get:
0.0118 < p < 0.0576
Therefore, the best choice is C.

Use the Given Degree of Confidence and Sample Data to Construct