Question

A market analyst wants to know if the new website (Website A) he designed is showing increased page view per visit than his original website (Website B). A customer is randomly sent to one of the two different websites, offering the same products. Here are the summary statistics for the page views for each website.

Website 1	Wesite 2
12	8
4	12
14	3
10	4
2	5

a. State/check the conditions for the appropriate hypothesis test. Be sure to take note of the histograms shown above.

b. Run the appropriate hypothesis test. State the hypotheses, test statistic with degrees of freedom, p-value in terms of the test statistic and conclusion with context based on a 5% significance level.

c. Construct and interpret, using context, a 95% confidence interval for the difference in the population means of page views for each website.

Answer 1

Website 1	Wesite 2
12	8
4	12
14	3
10	4
2	5
8.4	6.4	mean
5.176872	3.646917	sd

The following null and alternative hypotheses need to be tested: Ho: 1 2 Ha:1 2 This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the degrees of freedom are df 8. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal: = 8 Hence, it is found that the critical value for this right-tailed test is te = 1.86, for a = 0.05 and df The rejection region for this right-tailed test is R {t : t > 1.86}. (3) Test Statistics Since it is assumed that the population variances are equal, the t-statistic is computed as follows: XI- X2 (n1-1)S3+(n2-1)s + n2 n1+n2-2 8.4 6.4 = 0.706 (5-1)5.1768722+(5-1)3.6469172 5+5-2 (4) Decision about the null hypothesis Since it is observed that t 0.706 < te = 1.86, it is then concluded that the null hypothesis is not rejected. 0.25, and since p = 0.25 > 0.05, it is concluded that Using the P-value approach: The p-value is p the null hypothesis is not rejected

(5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean 1 is greater than 2, at the 0.05 significance level. Confidence Interval The 95% confidence interval is -4.531 <1