​Co-browsing refers to the ability to have a contact center agent and customer jointly navigate an...

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​Co-browsing refers to the ability to have a contact centeragent and customer jointly navigate an application on a real timebasis through the web. A study of businesses indicates that 88 of126 ​co-browsing organizations use​ skills-based routing to matchthe caller with the right​ agent, whereas 61of 180 ​non-co-browsingorganizations use​ skills-based routing to match the caller withthe right agent.

a. At the0.01 level of​ significance, is there evidence of adifference between​ co-browsing organizations and​ non-co-browsingorganizations in the proportion that use​ skills-based routing tomatch the caller with the right​ agent? Let π1represent theproportion of​ co-browsing organizations, and let π2 represent theproportion of​ non-co-browsing organizations. What are the null andalternative hypotheses to​ test?

calculate the test statistic

x2stat =

What is the critical value for .01

x2 .01 =

b. The p-value =

b. An earlier​ Z-test for the difference between two proportionsin parts​ (a) and​ (b) resulted in a test statistic of ZSTAT=6.19against critical values of −2.33 and 2.33 with a​ p-value of .000.Compare the results of​ (b) and​ (c) to the results of the​Z-test.

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4.2 Ratings (843 Votes)

a)

null hypothesis: Ho:Ï€1=Ï€2

alternative hypotheses Ha:π1 ≠π2

Applying chi square test of independence:
Observed co-browsing Non Total
use 88 61 149
not use 38 119 157
total 126 180 306
Expected Ei=row total*column total/grand total co-browsing Non Total
use 61.3529 87.6471 149.00
not use 64.6471 92.3529 157.00
total 126.00 180.00 306.00
chi square    χ2 =(Oi-Ei)2/Ei co-browsing Non Total
use 11.573 8.101 19.6749
not use 10.984 7.6886 18.6723
total 22.5572 15.7900 38.347
test statistic X2 = 38.3472
degree of freedom(df) =(rows-1)*(columns-1)= 1
for 1 df and 0.01 level , critical value       χ2= 6.635

b)

from excel: p value =chidist(38.3472,1) =0.0000

b)

both distribution reject the null hypothesis since both have test statistic is in the critical region


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