Final answer:
To construct a confidence interval for a population proportion using sample data and given degree of confidence, you can follow a few steps. In this case, the 95% confidence interval for the population proportion is (0.795, 0.867).
Step-by-step explanation:
To construct a confidence interval for a population proportion, we can use the formula: p' ± EB
Step 1:
Calculate p', the estimated proportion of successes, by dividing the number of successes (x) by the sample size (n): p' = x/n
Step 2:
Calculate the error bound (EBP) using the formula: EBP = Z * √(p'(1-p')/n), where Z is the z-score corresponding to the desired confidence level.
Step 3:
Construct the confidence interval by subtracting the error bound from p' and adding it to p': (p' - EBP, p' + EBP).
In this case, p' = 162/195 = 0.831. Since the degree of confidence is 95%, the corresponding z-score is approximately 1.96. Using these values, we can calculate the error bound (EBP): EBP = 1.96 * √(0.831 * (1-0.831)/195) ≈ 0.036.
Thus, the confidence interval for the population proportion is approximately (p' - EBP, p' + EBP) = (0.831 - 0.036, 0.831 + 0.036) = (0.795, 0.867).