Final answer:
The 95% confidence interval for the proportion of students who like statistics is determined using the formula with the sample proportion and the standard error, which is calculated to be approximately (0.1651, 0.3349), or (0.17, 0.33) when rounded.
Step-by-step explanation:
To determine the 95% confidence interval for the proportion of students who like statistics, we utilize the sample proportion (p') and calculate the margin of error using the critical value z that corresponds to the 95% confidence level (which is approximately 1.96 for a two-tailed test) and the standard error of the proportion. The standard error (SE) is given by the formula SE = sqrt[(p'*(1-p'))/n], where n is the sample size. In this example, with 25 out of 100 students liking the subject, our sample proportion (p') is 0.25. Using these values, we calculate the SE as sqrt[(0.25*0.75)/100] = 0.0433.
The margin of error (EBP) is then EBP = z*SE, which yields EBP = 1.96 * 0.0433 = 0.0849. Therefore, the 95% confidence interval is p' ± EBP, equating to 0.25 ± 0.0849, or (0.1651, 0.3349).
Rounding to two decimal places, the 95% confidence interval for the population proportion of students liking statistics is (0.17, 0.33). Therefore, the correct option is O CI (0.16, 0.33).