Confidence Intervals

point estimate

value of sample statistic corresponding with the parameter (p-hat or x-bar)

level of confidence

probability of the interval capturing the population parameter (P or M)

confidence interval

set of values estimating the true parameter (proportion or mean)

confidence interval for proportion conditions 

1. random & independent

2. n(phat) and n(qhat) > / = to 10

how to narrow a confidence interval

• decrease the confidence level

• increase sample size

______ the confidence level _____ the confidence interval

increasing, widens

with a ______ sample size, the interval becomes ______

larger, narrower

steps to constructing a confidence interval for proportion

1. phat

2. conditions 

3. Find Z_a/2

4. MOE

5. phat ± MOE

6. write an interpretation 

As sample size gets ______ the student t distribution becomes closer to standard normal

larger

Confidence Interval for Mean critical value 

t_a/2 with df= n-1

Since Population SD isnt known, what do you use instead? 

“s” in place of sigma

t distribution estimates standard deviation so it includes _____ uncertainty leading to a ______ confidence interval

greater, wider