Question

In a recent tennis tournament, women playing singles matches used challenges on 133 calls made by the line judges. Among those challenges, 31 were found to be successful with the call overturned. What is the estimated success rate of challenges with a 95% confidence interval?

Option 1: 19.82% (18.61%, 21.03%)
Option 2: 23.31% (21.98%, 24.64%)
Option 3: 17.25% (16.04%, 18.46%)
Option 4: 22.15% (20.78%, 23.52%)

Answer 1

To find the estimated success rate of challenges with a 95% confidence interval, divide the number of successful challenges by the total challenges and calculate the margin of error using the standard error. The correct option is Option 2: 23.31% (21.98%, 24.64%).

Step-by-step explanation:

To find the estimated success rate of challenges with a 95% confidence interval, we can use the formula for estimating a proportion:

Success rate = (Number of successful challenges / Total challenges) * 100%

Using the given information, the success rate is (31 / 133) * 100% = 23.31%.

To calculate the 95% confidence interval, we can use the formula:

Lower bound = Success rate - Margin of error

Upper bound = Success rate + Margin of error

The margin of error is calculated as:

Margin of error = Critical value * Standard error

Using a 95% confidence level, the critical value is 1.96 (for a sample size greater than 30).

Using the formula for the standard error:

Standard error = √(Success rate * (1 - Success rate) / Total challenges)

Plugging in the values, the standard error is √((0.2331 * 0.7669) / 133). This results in a standard error of approximately 0.025.

So, the 95% confidence interval is 23.31% ± (1.96 * 0.025), which gives us the range of (21.98%, 24.64%). Therefore, the correct option is Option 2: 23.31% (21.98%, 24.64%).