Final answer:
The point estimate of the proportion of successful challenges is 0.3667. The 95% confidence interval for the proportion is [0.3064, 0.4270]. With 95% confidence, we cannot conclude that more than half of all American adults believe this. The 75% confidence interval is [0.3434, 0.3899]. With 75% confidence, we can conclude that at least half of all American adults believe this.
Step-by-step explanation:
To construct a confidence interval for the proportion of successful challenges, we need to find the point estimate and the error bound.
The point estimate is the ratio of successful challenges to total challenges: 88/240 = 0.3667.
The error bound can be calculated using the formula: E = Z * sqrt((p * (1-p))/n), where Z is the critical value, p is the point estimate, and n is the total number of challenges.
For a 95% confidence level, the critical value Z is approximately 1.96.
Substituting the values into the formula, we get: E = 1.96 * sqrt((0.3667 * (1-0.3667))/240) = 0.0603.
Therefore, the 95% confidence interval is [0.3667 - 0.0603, 0.3667 + 0.0603] = [0.3064, 0.4270].
b. With 95% confidence, we cannot conclude that more than half of all American adults believe this, since the lower bound of the confidence interval is below 0.5.
c. To calculate a 75% confidence interval, we use n = 1000 and the same point estimate of 0.3667. We can calculate the error bound using the formula: E = 0.922 * sqrt((0.3667 * (1-0.3667))/1000) = 0.0233.
The 75% confidence interval is [0.3667 - 0.0233, 0.3667 + 0.0233] = [0.3434, 0.3899]. With 75% confidence, we can conclude that at least half of all American adults believe this, since the lower bound of the confidence interval is above 0.5.
The Question is incomplete. The complete question is
Tennis Challenges In a recent U.S. Open tennis tournament, men playing singles matches used challenges on 240 calls made by the line judges. Among those challenges, 88 were found to be successful with the call overturned. Construct a 95% confidence interval for the propor-tion of successful challenges