One of the biggest issues facing e-retailers is the ability to turn browsers int

Question

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 sample of 200 browsers at the redesigned site was selected. Suppose that 17 browsers made a purchase. The company officials would like to know if there is evidence of a decrease in conversion rate at the 5% level of significance. 8. a. Use the critical value approach and interpret the test result. b. Use the p-value approach and interpret the test result

Explanation / Answer

here null hypothesis: Ho: p>=0.101

alternate hypothesis:Ha: p<0.101

a) critical value approach: for 5% level and left tail test ; critical value z=-1.645

Decision rule:reject null hypothesis if test statistic z<-1.645

for n=200 ; std error =(p*(1-p)/n)1/2 =0.0213

sample proportion phat =17/200=0.085

therfore test statistic z=(phat-p)/std error =(0.085-0.101)/0.0213 =-0.7509

for test statistic is not less then crtiitcal value; we fail to reject null hypothesis

we do not have sufficient evidence of a decrease in conversion rate at the 5% level of significance.

b)

for above test statistic and left tailed test p value =0.2263

as p value is higher then 5% level of significance ;we fail to reject null hypothesis

we do not have sufficient evidence of a decrease in conversion rate at the 5% level of significance.

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