Final answer:
To calculate the 98% confidence interval for a sample proportion, use the formula p ± Z * sqrt((p*(1-p))/n), where p is the sample proportion, n is the sample size, and Z is the Z-score corresponding to the desired confidence level. In this case, the confidence interval is (35.3%, 42.9%).
Step-by-step explanation:
To calculate the 98% confidence interval for a sample proportion, we can use the formula:
p ± Z * sqrt((p*(1-p))/n)
where p is the sample proportion, n is the sample size, and Z is the Z-score corresponding to the desired confidence level.
In this case, the sample size is 366 and the number of successes is 143, so the sample proportion is 143/366 = 0.391. The Z-score for a 98% confidence level is approximately 2.326.
Plugging in the values:
0.391 ± 2.326 × sqrt((0.391 × (1-0.391))/366)
Simplifying the expression gives us the confidence interval (0.353, 0.429) or (35.3%, 42.9%). This means that we can be 98% confident that the true population proportion lies between 35.3% and 42.9%.