× / D STAT 513-001 HWAndr × \\ Chegg Siudy | Guided 5, x \\ à STAT 513-001 HW3.p

Question

× / D STAT 513-001 HWAndr × Chegg Siudy | Guided 5, x à STAT 513-001 HW3.pd1 _ clù people.statsc.eduwang528/Stat%20513/5 IAI %20513-001%20HWA.pdf Apps Pig Rank King of the ::: STAT 513-001 HW4.pdf 3 /3 Using a chemical procedure called differential pulse polarograply, a chemist measured the peak current gencrated (in microamperes, MA) when solutions containing different amounts of nickel (measured in parts per billion, ppb) are added to different portions of the same buffer. Is there sufficient evidence to indicate that peak current increases as nickel concentrations increase? Use .05 x = Ni (ppb) y = Peak Current (11A) 19.1 38.2 57.3 76.2 95 114 131 150 170 .095 174 256 348 429 500 580 651 722 In addition, complete the following parts: 1. Compute a 95 percent confidnval fo the mean peak current when the nickel concen- tration is r100 ppb. Interpret the interval. 2. Compute a 95 peet confidence interval for the peak current when the nickel concentration is z. = 100 ppb. Interpret the interval. 3. Compare the two intervals. Which interval is wider? Why? Type here to search w 9:30 PM 10y16/2017

Explanation / Answer

Let's used Minitab to find confidence limit (for mean) and prediction limit (for predicted value) Peak Current when the nickel concentration is x = 100 ppb.

Step 1) First enter the given data set in minitab columns.

Step 2) Click on Stat>>>Regression>>>General regression...

Response: select y

Model: select x

Step 3) Click on Prediction

in "New observation for continuous predictors:

we want to predict y for given x = 100

So put 100

Select confidence limits:

and prediction limits

Then click on OK

then click on Option.

Confidence level for all interval: put 95

Types of confidence interval: Two-sided.

then click on OK and again Click on OK

So we get the following minitab output

General Regression Analysis: y versus x_1

Regression Equation

y = 0.0190223 + 0.0042222 x_1

Coefficients

Term Coef SE Coef T P
Constant 0.0190223 0.0065728 2.8941 0.023
x_1 0.0042222 0.0000620 68.0643 0.000

Summary of Model

S = 0.00898775 R-Sq = 99.85% R-Sq(adj) = 99.83%
PRESS = 0.00109129 R-Sq(pred) = 99.71%

Analysis of Variance

Source DF Seq SS Adj SS Adj MS F P
Regression 1 0.374232 0.374232 0.374232 4632.75 0.0000000
x_1 1 0.374232 0.374232 0.374232 4632.75 0.0000000
Error 7 0.000565 0.000565 0.000081
Total 8 0.374798

Fits and Diagnostics for Unusual Observations

Obs y Fit SE Fit Residual St Resid
9 0.722 0.736796 0.0055696 -0.0147955 -2.09745 R

R denotes an observation with a large standardized residual.

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 0.441242 0.0030166 (0.434109, 0.448375) (0.418824, 0.463660)

Values of Predictors for New Observations

New Obs x_1
1 100

a) From the above output 95% confidence interval for the mean peak current when the nickel concentration is x = 100 ppb. is (0.434109, 0.448375)

b) The 95% confidence interval for the peak current when the nickel concentration is x = 100 ppb. is same as the prediction interval (0.418824, 0.463660)

c) From part a) and b) we conclude that the prediction interval is wider than the mean interval because the standard error of mean is smaller than the standard error of predicted value.

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