The management of a water park has concerns about the chlorine level of 0.4% mg/mL increasing to an unsafe level.The management tests the hypothesis that the park's chlorine proportions have remained the same.An independent agency ran a test on a random sample size of $10000$ and found the chlorine level at 0.5% mg/mL.Create a 95% confidence interval for the proportion of chlorine in the water.
A)Based on the data,we are 95% confident the proportion of chlorine in the water is between 0.102% and 0.898%.
B)Based on the data,we are 95% confident the proportion of chlorine in the water is between 0.109% and 0.891%.
C)Based on the data,we are 95% confident the proportion of chlorine in the water is between 0.362% and 0.638%.
D)Based on the data,we are 95% confident the proportion of chlorine in the water is between 0.009% and 0.891%.
E)Based on the data,we are 95% confident the proportion of chlorine in the water is between 0.4% and 0.6%.

Question

Quizplus · Accepted Answer

The sample proportion is 0.5%. Using the formula for a confidence interval for a proportion, the interval is calculated as 0.5% ± 1.96 * sqrt((0.5% * (1 - 0.5%)) / 10000), which results in the interval 0.362% to 0.638%.

The Management of a Water Park Has Concerns About the Chlorine