STS 110 Lecture Notes - Lecture 20: Confidence Interval, Sample Size Determination
27 Apr 2018
School
Department
Course
Professor
Confidence intervals
1- Understand a confidence interval
2- Understand a confidence level
3- Be able to construct a confidence interval on stat crunch
4- Interpreting a confidence interval
1.) Understand a confidence interval
Recall:
n: sample size
x: sample mean
u: population mean
Letās estimate the mean # of phone contacts all STS110 students have.
ļ not practical to get the mean for all STS110 students
ļ sample 30 students and get a sample mean of 487.4
487.4 is the estimate.
Is this u?
No, itās oī
¶ly a sī
µall saī
µple
- Better way to estimate mean is 487.4 with a margin of error of 100.
- (387.4,587.4) ļ confidence interval
- a confidence interval is a range of numbers likely, but not guaranteed, to contain the
population mean.
- (lower limit, upper limit)
- (sample mean ā margin of error, sample mean + margin of error)
Ex: sample mean weight = 160 pounds
Margin of error = 5 pounds
Sample size = 50 women
(155 lbs,165 lbs)
ALWAYS USE UNITS!
Ex: A confidence interval to estimate heights of men is given by (65 in, 72 in)
1- find sample mean: 68.5 in
2- find margin of error: 3.5 in
3- find population mean: cannot find this
4- find sample size: cannot find this
2.) Understand a confidence level
A percentage assigned to a confidence interval that locates how well it estimates the
population mean.
Estimate weights of women at Elon.
1) (140 lbs, 142 lbs)
2) (130 lbs, 150 lbs)
3) (100 lbs, 200 lbs) ļ best estimate
4) (0 lbs, 500 lbs)
- you generally want to be between 90% - 99% to provide a good and strong
confidence interval.
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
3- be able to construct a confidence interval on stat crunch. Recall: n: sample size x: sample mean u: population mean. Let"s estimate the mean # of phone contacts all sts110 students have. Not practical to get the mean for all sts110 students. Sample 30 students and get a sample mean of 487. 4. Better way to estimate mean is 487. 4 with a margin of error of 100. A confidence interval is a range of numbers likely, but not guaranteed, to contain the (387. 4,587. 4) confidence interval population mean. (lower limit, upper limit) (sample mean margin of error, sample mean + margin of error) Sample size = 50 women (155 lbs,165 lbs) Ex: a confidence interval to estimate heights of men is given by (65 in, 72 in) A percentage assigned to a confidence interval that locates how well it estimates the population mean.
