Question

Does​ co-browsing have positive effects on the customer​ experience? Co-browsing refers to the ability to have a contact center agent and customer jointly navigate an online document or mobile application on a​ real-time basis through the web. A study of businesses indicates that 8080 of 139139 ​co-browsing organizations use​ skills-based routing to match the caller with the right​ agent, whereas 8585 of 167167 ​non-co-browsing organizations use​ skills-based routing to match the caller with the right agent. Complete parts​ (a) and​ (b) below. a. At the 0.010.01 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? State the null and alternative​ hypotheses, where pi 1π1 is the population proportion of​ co-browsing organizations that use​ skills-based routing and pi 2π2 is the population proportion of​ non-co-browsing organizations that use​ skills-based routing.

Answer 1

There is not enough evidence to support the claim that there is 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 (P-value=0.1191).

Explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is 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.

Then, the null and alternative hypothesis are:

`H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\\eq 0`

The significance level is 0.01.

The sample 1 (co-browsing), of size n1=139 has a proportion of p1=0.576.

`p_1=X_1/n_1=80/139=0.576`

The sample 2 (non-co-browsing), of size n2=167 has a proportion of p2=0.509.

`p_2=X_2/n_2=85/167=0.509`

The difference between proportions is (p1-p2)=0.067.

`p_d=p_1-p_2=0.576-0.509=0.067`

The pooled proportion, needed to calculate the standard error, is:

`p=(X_1+X_2)/(n_1+n_2)=(80.064+85.003)/(139+167)=(165)/(306)=0.833`

The estimated standard error of the difference between means is computed using the formula:

`s_(p1-p2)=\sqrt{(p(1-p))/(n_1)+(p(1-p))/(n_2)}=\sqrt{(0.833*0.167)/(139)+(0.833*0.167)/(167)}\\\\\\s_(p1-p2)=√(0.001+0.00083)=√(0.00184)=0.0429`

Then, we can calculate the z-statistic as:

`z=(p_d-(\pi_1-\pi_2))/(s_(p1-p2))=(0.067-0)/(0.0429)=(0.067)/(0.0429)=1.56`

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

`P-value=2\cdot P(t>1.56)=0.1191`

As the P-value (0.1191) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is 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.