A Today/CNN/Gallup Poll of 1015 adults found that 13% approved of the job Congress was doing in 1995. Find the 95% confidence interval of the true proportion of adults who feel this way.
To find the 95% confidence interval of the true proportion of adults who approve of the job Congress is doing, we can use the formula for calculating a confidence interval for a population proportion.
The formula for a confidence interval for a proportion is given by:
CI = p̂ ± Z * √( (p̂ * (1-p̂)) / n )
Where:
- CI is the confidence interval
- p̂ is the sample proportion (13% or 0.13)
- Z is the critical value corresponding to the desired level of confidence (95% confidence level corresponds to a Z-value of approximately 1.96)
- n is the sample size (1015)
Now let's plug in the values into the formula:
CI = 0.13 ± 1.96 * √( (0.13 * (1-0.13)) / 1015 )
Calculating this formula will give us the confidence interval, which represents the range within which we can be 95% confident that the true proportion of adults who approve of the job Congress is doing falls.