Thirty five percent of adult americans are regular voters. A random sample of 250 adults in a medium size college town were surveyed, and it was...Estimate the true proportion of regular voters with 90% confidence and comment on the results.
To estimate the true proportion of regular voters with 90% confidence, we can use the method of confidence interval.
Step 1: Define your parameters:
Let's define the proportion of regular voters in the population as "p". We want to estimate the true value of "p" with a level of confidence of 90%.
Step 2: Calculate the sample proportion:
In the survey, a random sample of 250 adults was surveyed. Let's say that "x" out of 250 adults in the sample were regular voters. We can calculate the sample proportion of regular voters as the number of regular voters in the sample divided by the total sample size, which is x/250.
Step 3: Calculate the standard error:
The standard error (SE) is a measure of the variability of the sample proportion. To calculate the standard error, we can use the formula: SE = √((p*(1-p))/n), where "p" is the sample proportion and "n" is the sample size.
Step 4: Calculate the margin of error:
The margin of error represents the maximum difference between the sample proportion and the true proportion. It can be calculated as the product of the critical value (Z) and the standard error (SE). For a 90% confidence level, the critical value is 1.645 (lookup from a Z-table).
Step 5: Calculate the confidence interval:
The confidence interval is calculated as the sample proportion plus/minus the margin of error. Mathematically, it can be represented as: Confidence Interval = Sample Proportion ± Margin of Error.
Using the above steps, we can calculate the confidence interval for the true proportion of regular voters.
I hope this explanation helps you understand the process of estimating the true proportion with confidence interval. If you know the sample proportion (x/250) from the survey, you can follow the steps mentioned above to calculate the confidence interval and estimate the true proportion of regular voters.