Download T-Intervals for Means

Confidence Intervals - Day 3 - COMPLETE
T-Intervals for Means
Whatdowedoifwedon'tknowσ?Howmightthe
con5idenceintervalchange?
Confidence Intervals - Day 3 - COMPLETE
Confidence Intervals - Day 3 - COMPLETE
Degrees of Freedom and the Critical Value
When using a t-distribution we have to make adjustments due to not knowing the
population standard deviation.
We say we have (n-1) degrees of freedom and the more degrees we have the
closer it becomes to the Standard Normal Curve.
In the picture below the graph with 5 d.f. is closer to the Standard Normal Curve
when compared with the graph of 2 d.f.
Confidence Intervals - Day 3 - COMPLETE
Use Table B to find the critical value t* (our textbook uses the notation t c) that
you would use for a confidence interval for a population mean µ in of the
following situations.
a) 98% confidence interval based on n = 22 observations.
b) 90% confidence interval from a SRS of 10 observations.
c) 95% confidence interval from a SRS of 7 observations.
d) 96% confidence interval based on n = 67 observations.
e)99%con5idenceintervalfromasampleofsize56
f)80%con5idenceintervalfromasampleofsize150
g)85%con5idenceintervalfromasampleofsize18
h)99.9%con5idenceintervalforanSRSof8observations.
Confidence Intervals - Day 3 - COMPLETE
Remember all confidence intervals have the same format:
Estimate ± Margin of Error
When we don't know the population standard deviation,σ, we alter
our margin of error formula to use the sample standard deviation
and t*.
Remember when finding t*, you need to use n-1 degrees of freedom on the chart!!!!
Confidence Intervals - Day 3 - COMPLETE
Constructa98%con5idenceintervalforthemeanamountof
acetylsalicylicacidinthetablets.
Confidence Intervals - Day 3 - COMPLETE
Acerealmaker’scontainermachineisdesignedto5illboxessothatthemean
weightofcerealintheboxesis18ounces.Asimplerandomsampleof30
boxesproducedbythemachineyieldsameanweightof17.92ouncesanda
samplestandarddeviationof0.2ounces.Constructandinterpreta90%
con5idenceintervaltoestimatethetruemeanweightofcerealintheboxes.
Thelevelofdissolvedoxygeninariverisanimportantindicatorof
thewater'sabilitytosupportaquaticlife.Youcollectwatersamples
at15randomlychosenlocationsalongastreamandmeasurethe
dissolvedoxygen.Hereareyourresultsinmilligramsperliter:
Constructandinterpreta95%con5idenceintervaltoestimatethe
meandissolvedoxygenlevelinthisstream.
Confidence Intervals - Day 3 - COMPLETE
p. 323 # 1-15 odds, 33