A researcher wants to estimate the proportion of a population which possesses a given characteristic. A random sample of size 250 is taken and 40% of the sample possesses the characteristic. The 95% confidence interval to estimate the population proportion is
thats wrong
.37 to .46
To calculate the 95% confidence interval for estimating the population proportion, we need to use the formula for a confidence interval for proportions. The formula is:
Confidence Interval = sample proportion ± (critical value * standard error)
Where:
- The sample proportion is the observed proportion in the sample (40% in this case).
- The critical value is determined by the desired confidence level (95% in this case). For a 95% confidence level, the critical value is approximately 1.96.
- The standard error is the measure of the variability in the sample proportion. It is calculated as the square root of [(sample proportion * (1 - sample proportion)) / sample size].
Using the given information, we can calculate the confidence interval as follows:
Sample Proportion = 40% = 0.4
Critical Value (z) = 1.96
Sample Size (n) = 250
Standard Error (SE) = √[(0.4 * (1 - 0.4)) / 250]
SE = √[(0.4 * 0.6) / 250]
SE = √(0.24 / 250)
SE ≈ 0.0346
Now we can calculate the confidence interval:
Confidence Interval = 0.4 ± (1.96 * 0.0346)
Confidence Interval = 0.4 ± 0.0678
Therefore, the 95% confidence interval to estimate the population proportion is approximately 0.3322 to 0.4678.