Final answer:
To construct a confidence interval for a binomial experiment, we can use the normal distribution approximation. Use the sample proportions to find the point estimate for a 95% confidence interval. Calculate the error bound using the formula: error bound = z-value * sqrt[(p-hat)(1-p-hat)/n].
Step-by-step explanation:
To construct a confidence interval for a binomial experiment, we can use the normal distribution approximation. Since the sample size is large enough and the success/failure condition is satisfied, we can use the normal distribution.
To find the point estimate for a 95% confidence interval, we first calculate the sample proportion for each experiment. In the first experiment, the sample proportion is 65/71 = 0.9155, and in the second experiment, the sample proportion is 39/58 = 0.6724.
The z-value for a 95% confidence interval is approximately 1.96. Now we can calculate the error bound using the formula: error bound = z-value * sqrt[(p-hat)(1-p-hat)/n].