91Ó°ÊÓ

Permeation Sampling. Permeation sampling is a method o sampling air in buildings for pollutants. It can be used over a long period of time and is not affected by humidity, air currents, or temperature. In the paper "Calibration of Permeation Passive Samplers With Silicone Membranes Based on Physicochemical Properties of the Analytes" (Analytical Chemistry, Vol. 75, No, 13, pp. 3182-3192). B. Zabiegata et al. obtained calibration constants experimentally for samples of compounds in each of four compound groups. The following data summarize their results.

At the $5\%$significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean calibration constant among the four compound groups? (Note:,$T_3=0.870,T_4=0.499$,$\mathrm{Î\pounds }{x}_i^2=0.456919$)

Step by step solution

01

Given information

The given data is

$T_1=0.638$

$T_2=1.206$

$T_3=0.870$

$T_4=0.499$

$\mathrm{Î\pounds }{x}_i^2=0.456919$.

02

Explanation

Using the given data, find SST, SSRT, SSE with the relation

$SST=∑x^2-\frac{{\left(∑x\right)}^2}{n}$

$SST=0.4569-\frac{(3.2130{)}^2}{25}$

$=0.0440$

$SSTR=\frac{∑{\left(x_i\right)}^2}{n_i}-\frac{{\left(∑x\right)}^2}{n}$

$=\frac{0.{0901}^2}{5}+\frac{0.{1558}^2}{10}+\frac{0.{1439}^2}{6}+\frac{0.{0672}^2}{4}-\frac{(3.2130{)}^2}{25}$

$SSTR=0.0023$

$SSE=SST-SSTR$

$=0.0417$

Then,

$d{f}_T=k-1$

$=4-1$

$=3$

$d{f}_E=n-k$

$=25-4$

$=21$

$MSTR=\frac{SSTR}{d{f}_T}$

$=\frac{0.0023}{3}$

$=0.00077$

$MSE=\frac{SSE}{d{f}_E}$

$=\frac{0.0417}{21}$

$=0.001986$

$F=\frac{MSTR}{MSE}$

$=\frac{0.00077}{0.001986}≈0.3877$

Let's create the ANOVA table

Data do not provide sufficient evidence at the $5\%$significance level since the $p-$value fails to reject the null hypothesis.

$P>0.05⇒FailtoReject{H}_0$.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!