Date on the rate at whicn volatile liquid will spread Ecross a surface are in th

Question

Date on the rate at whicn volatile liquid will spread Ecross a surface are in the table. Complete parts a through c ·Find 90% confidence interval for the me n mass of all spils with an elapsed time of 39 minutes. Interpret the result. Time (inutes} What is the contidenc.e interval? Mase (Pounds 6.65 5.97 5.44 Round lo three decimal paces as necded) Interpret the result Choose the correct answer below. O A. Wg dre 90% confident that the interval will not contain the mean rnass of the spill at 39 minutes. 451 B. We are 90% confident that the interval will contain the mean mass of the spill after 39 minutes 3 13 2 82 241 2.07 1.53 0.91 0.19 14 O c. D. we are 90% confident that the interval will contain 39 minutes 18 We are 90% confident that the interval will contain the mean mass of the spill before 39 minutes has passed. b. Find a 90% prediction interval forte mass of a single spil with an elapsed time of 39 minutes interpret tne result What is the prediction interval? Round to three decimal places as needed.)

Explanation / Answer

time <- c(0,2,4,6,8,10,12,14,16,18,20,25,30,45,60)
mass <- c(6.65,5.97,5.44,5.02,4.51,3.94,3.56,3.13,2.82,2.41,2.07,1.53,0.91,0.19,0)

fit <- lm(mass~time)

summary(fit)

newdata<- data.frame(time=39)

## confidencen interval
predict(fit, newdata, interval="confidence",level = 0.90)

## prediction interval
predict(fit, newdata, interval="predict",level = 0.90)

The results are

> predict(fit, newdata, interval="confidence",level = 0.90)
fit lwr upr
1 0.8146841 0.1573533 1.472015

Thus we are 90% confident that the interval will contain the mean mass of 39 minutes
>
> ## prediction interval
> predict(fit, newdata, interval="predict",level = 0.90)
fit lwr upr
1 0.8146841 -0.8612181 2.490586

the prediction interval is wider , you can calculate the width by

upperlimit - lower limit

hence the width of the prediction interval is more

This willalways be the case  The key point is that the confidence interval tells you about the likely location of the true population parameter.Prediction intervals must account for both the uncertainty in knowing the value of the population mean, plus data scatter , hence more error means more wide

prediction interval is an estimate of an interval in which future observations will fall,

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