Warm-up9.1 Confidence Interval of the Mean

Answers to H.W. Discussion Questions

9.1 Confidence Interval for a Mean

S.E. for Proportion S.E. for Mean

95% C.I. for a Proportion 95% C.I. for a Mean

97.8 98.0 98.2 98.2 98.2 98.6 98.8 98.8 99.2 99.4The mean body temperature, ,for this sample of ten

women is 98.52, and the standard deviation, s, is 0.527. What is the confidence interval for this sample?We don’t have the σ for the population. : (

n

pp )1( n

n

ppp

)1(96.1

nx

96.1

x

How to find when it is not known.

When the assumptions and conditions are met, we cancalculate the confidence interval.

. The critical value t*n -1 depends on the

confidence interval you specify and on the degrees of freedom (n-1), which you get from the sample size.

)(1* xSEtx n

n

sxSE )(

Finding the confidence interval from a list of data97.8 98.0 98.2 98.2 98.2 98.6 98.8 98.8 99.2 99.4

Finding the confidence interval from the mean and s.d. of a sampleWhenever you construct a confidence interval based on t, there arethree conditions you must check. Officially, you need a random sample (or random assignment of treatments to units) that i approximately normally or a large enough sample size that the distribution of thesample mean is approximately normal. In the case of a survey, the sizeof the population should be at least ten times the size of the sample.

(Listed in detail on pg 569 of textbook)

ProblemResidents of a community are concerned of the vehiclespeed on a road called Triphammer. One particular day

theresidents gather the speed of 23 cars. Once the data isgathered, a histogram is created and it appearsapproximately normal. Describe the conditions.

Solve for the confidence interval anyway.

25.40.3123 smphxcarsn

Describe the confidence interval in the context and M.E.

Common Quiz MistakesMargin of Error = z* S.E. Form A = +3.5%; Form B = + 14%

Step 3 of #2 When drawing the distribution curve, you need to divide

the alpha and find the critical value.Form A (alpha = 0.01, 0.005 on both sides with a critical

value of + 2.570Form B (alpha = 0.05, 0.025 on both sides with a critical

value of + 1.96 on both sides)