The Basics
A statistic that provides an estimate of a population parameter
Point Estimator
Point estimate +/- Margin of error
Confidence Level
Step 1 of:
A recent poll found that 433 of the 1548 randomly-selected U.S. adults questioned felt that unemployment compensation should be extended an additional six months while the country is in its current economic downturn. Use this information to construct a 95% confidence interval to estimate the proportion of the U.S. adults who feel this way
we will estimate the true proportion of U.S. adults who will feel that unemployment compensation should be extended an additional six months while the country is in its current economic downturn with a 95% confidence level
What are the 4 steps in the 4 step process
State, Plan, Do, Conclude
The difference between the point estimate and true parameter value will be less than this value in C% of all samples
Margin of Error
n <= N/10
10% condition
Step 1 of:
A random sample of students who took the SAT college entrance examination twice found that 427 of the respondents had paid for coaching courses and that the remaining 2733 had not. Construct and interpret a 99% confidence interval for the proportion of coaching among students who retake the SAT.
we will estimate the true proportion of coaching among students who will retake the SAT with 99% confidence
The command used to find z* and the command to find t*
invNorm()
invT()
The range of possible true means/proportions at a certain confidence level
Confidence Interval
np>= 10 and n(1-p) >= 10
Large Counts Condition
If a free response question asks you to construct and interpret a confidence interval, what does that mean
4-step process
Write a conclusion for the 99% confidence interval (.37, .42) where we are estimating the true proportion of sugar in a popular candy
We can be 99% confident that the interval (.37, .42) captures the true proportion of sugar in a popular candy
The overall success rate of the method for calculating the confidence interval
Confidence Level
p^ +/- z* sqrt((^p(1-^p))/n)
One-sample z interval
Check if conditions are met
Latoya wants to estimate what proportion of the seniors at her boarding high school like the cafeteria food. She interviews an SRS of 50 of the 175 seniors living in the dormitory. She finds that 14 think the cafeteria food is good.
No, the 10% condition is not met
Measurements in millimeters of a dimension on an srs of 16 of 200 crankshafts. Construct a 95% confidence interval of the true mean of the measurements.
224.12 224.001 224.07 223.982 223.989 223.961 223.960 224.089 223.987 223.976 223.902 223.980 224.098 224.057 223.913 223.999
(223.969, 224.035)
Interpretation of confidence interval (0,1) at a confidence level of 95% with the true mean being the parameter
We are 95% confident that the interval from 0 to 1 captures the true mean
sqrt((p(1-p))/n)
Standard deviation of p^
Are all conditions met
Tonya wants to estimate what proportion of her school's seniors plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom.
Yes
In a recent National survey of drug Use and Health, 2312 of 5914 randomly selected full-time U.S. college students were classified as binge drinkers
Construct a 99% confidence interval
(.375, .407)