TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site. The conversion rate for a company's website was 10.1%. The website at the company was redesigned in an attempt to increase its conversion rates. A samples of 200 browsers at the redesigned site was selected. Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8, the null hypothesis will be rejected if the test statistics is
A) greater than 1.645
B) less than 1.645
C) greater than -1.645
D) less than -1.645

Question

Quizplus · Accepted Answer

The null hypothesis in this case is that there is no increase in conversion rate after the website redesign. The alternative hypothesis is that there is an increase in conversion rate. We can use a one-tailed z-test to test this hypothesis.

The test statistic is calculated as:

z = (p - P) / sqrt(P(1-P)/n)

where P is the hypothesized value of the population proportion (in this case, the conversion rate before the website redesign), p is the sample proportion (the observed conversion rate after the redesign), and n is the sample size (200).

Under the null hypothesis, P = 0.101 (the original conversion rate). Plugging in the numbers, we get:

z = (0.12 - 0.101) / sqrt(0.101*0.899/200) = 1.902

Since we are testing the alternative hypothesis that there is an increase in conversion rate, we are looking for a positive z-value.

From Table 9-8, the critical value for a one-tailed test at the 5% level of significance is 1.645. Since our calculated z-value (1.902) is greater than the critical value, we reject the null hypothesis and conclude that there is evidence of an increase in conversion rate at the 5% level of significance.

TABLE 9-8 One of the Biggest Issues Facing E-Retailers Is the Ability