Question

​Co-browsing refers to the ability to have a contact center agent and customer jointly navigate an application on a real time basis through the web. A study of businesses indicates that 88 of 126 ​co-browsing organizations use​ skills-based routing to match the caller with the right​ agent, whereas 61of 180 ​non-co-browsing organizations use​ skills-based routing to match the caller with the right agent.

a. At the0.01 level of​ significance, is there evidence of a difference between​ co-browsing organizations and​ non-co-browsing organizations in the proportion that use​ skills-based routing to match the caller with the right​ agent? Let π1represent the proportion of​ co-browsing organizations, and let π2 represent the proportion of​ non-co-browsing organizations. What are the null and alternative 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 proportions in parts​ (a) and​ (b) resulted in a test statistic of ZSTAT=6.19 against 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.

Answer 1

a)

null hypothesis: Ho:π1=π2

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