The St. Lucie County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the St. Lucie County Economic Development Board found that 20.8% of all county residents held at least a bachelor's degree. Find three different confidence intervals - one with sample size 487, one with sample size 777, and one with sample size 938. Assume that 20.8% of the county residents in each sample have earned at least a bachelor's degree. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=487n=487, the margin of error for a 95% confidence interval is given by . When n=487n=487, a 95% confidence interval is given by . When n=777n=777, the margin of error for a 95% confidence interval is given by . When n=777n=777, a 95% confidence interval is given by . When n=938n=938, the margin of error for a 95% confidence interval is given by . When n=938n=938, a 95% confidence interval is given by . If the sample size is increased, leaving all other characteristics constant, the margin of error of the confidence interval will . If the sample size is increased, leaving all other characteristics constant, the width of the confidence interval will.
The St. Lucie County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the St. Lucie County Economic Development Board found that 20.8% of all county residents held at least a bachelor's degree.
Find three different confidence intervals - one with
Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary.
- When n=487n=487, the margin of error for a 95% confidence interval is given by .
When n=487n=487, a 95% confidence interval is given by . - When n=777n=777, the margin of error for a 95% confidence interval is given by .
When n=777n=777, a 95% confidence interval is given by . - When n=938n=938, the margin of error for a 95% confidence interval is given by .
When n=938n=938, a 95% confidence interval is given by .
If the sample size is increased, leaving all other characteristics constant, the margin of error of the confidence interval will .
If the sample size is increased, leaving all other characteristics constant, the width of the confidence interval will.
Step by step
Solved in 3 steps
