(a) An insurance company wants to estimate the proportion of people unsatisfied with their new telephone help service. A survey of 200 callers revealed 45 were unsatisfied with the service. Construct by hand a 95% confidence interval for the proportion of unsatisfied customers.
45/200=.225 not satisfied (p-hat)
155/200=.775 satisfied(q -hat)
Standard dev.
The square root of (.225)(.775)/200
Margin of error = z-score times the sd
95% that leaves 5% with 2.5% in each tail or .025 which gives us a z-score from the table or from the calculator of 1.96
1.96 times the standard dev.
Add this number to the .225 and also subtract it from the .225 to get your confidence interval.