The range of possible values for the population parameter can be estimated using the margin of error, which is calculated as the critical value times the standard error.
Assuming a 95% confidence level, the critical value is approximately 1.96. The standard error for a sample proportion can be calculated as:
SE = sqrt[(p * (1 - p)) / n]
Where p is the sample proportion and n is the sample size. Substituting the values given in the question, we get:
SE = sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the standard error exactly. However, we can use a rule of thumb that states that if the sample size is at least 30, we can use the normal distribution to estimate the margin of error.
With a sample proportion of 0.65, the margin of error can be estimated as:
ME = 1.96 * sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the margin of error exactly. However, we can use the rule of thumb that a margin of error of about ±5% is typical for a 95% confidence level.
Using this margin of error, we can construct the following range of possible values for the population parameter:
0.65 ± 0.05
This range can be expressed as (0.6, 0.7), which corresponds to option A.
Therefore, the correct answer is option A) (0.6, 0.69).