To calculate the confidence interval, we'll use the formula:
CI = sample proportion ± z* (standard error)
where:
- sample proportion = p_hat = 23/50 = 0.46 (proportion of students in the sample who used tutoring and found it beneficial)
- z = 1.96 (for a 95% confidence level)
- standard error = sqrt(p_hat * (1 - p_hat) / n) = sqrt(0.46 * 0.54 / 50) = 0.101
Plugging these values into the formula, we get:
CI = 0.46 ± 1.96 * 0.101
CI = [0.263, 0.657]
Therefore, we can say with 95% confidence that the true proportion of Mesa students who have used tutoring and found it beneficial is between 0.263 and 0.657.