Question

A market analyst wants to know if the new website he designed is showing increased page views per visit. A customer is randomly sent to one of two different​ websites, offering the same​ products, but with different designs. The accompanying table shows the data from five randomly chosen customers from each website. Test the null hypothesis that the mean number of page visits is the same for the two websites. Assume that the data come from a population that is Normally distributed. Assume that the new website is website 1 and the old website is website 2. Complete parts a through f below.

a) Find the value of the​ t-statistic for the difference in sample mean page​ visits, y overbar 1 minus y overbar 2​, for the null hypothesis. tequals nothing ​(Round to three decimal places as​ needed.) ​b) Calculate the degrees of freedom from the formula dfequalsStartStartFraction left parenthesis StartFraction s Subscript 1 Superscript 2 Over n 1 EndFraction plus StartFraction s Subscript 2 Superscript 2 Over n 2 EndFraction right parenthesis squared OverOver StartFraction 1 Over n 1 minus 1 EndFraction left parenthesis StartFraction s Subscript 1 Superscript 2 Over n 1 EndFraction right parenthesis squared plus StartFraction 1 Over n 2 minus 1 EndFraction left parenthesis StartFraction s Subscript 2 Superscript 2 Over n 2 EndFraction right parenthesis squared EndEndFraction . dfequals nothing ​(Round to three decimal places as​ needed.) ​c) Calculate the degrees of freedom using the rule that dfequals​min(n1minus​1, n2minus​

Website 1	Website 2
9	9
12	12
11	2
8	6
2	5

1). dfequals nothing ​d) Find the​ P-value using the degrees of freedom from part b. pequals nothing ​(Use the answer from part b to find this answer. Round to four decimal places as​ needed.) ​e) Find the​ P-value using the degrees of freedom from part c. pequals nothing ​(Use the answer from part d to find this answer. Round to four decimal places as​ needed.) ​f) What do you conclude at alphaequals0.05​, if the null hypothesis Upper H 0 is that the mean number of page views is the same for both websites and the alternative hypothesis Upper H Subscript Upper A is that the mean number of page views is greater for website 1 than for website​ 2? ▼ Reject Fail to reject Upper H 0 for both cases. There ▼ is is not sufficient evidence to reject the claim that the mean number of page views is the same for both​ websites, in favor of the claim of increased page visits. Enter your answer in each of the answer b

Answer 1

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	9	9	0
	12	12	0
	11	2	9
	8	6	2
	2	5	-3
Average	8.4	6.8	1.6
St. Dev.	3.912	3.834	4.506
n	5	5	5

D bar =1.6

S_d = 4.506

Hypothesis :

μD​ = 0

μD​ not = 0 (Two tailed)

T Critical value :

Tc = 2.776 (df = n-1 = 4, α = 0.05) (From T table)

Rejection region :

|T stat| > 2.776, reject H0

Test :

T stat = D bar / (S_d/SQRT(n))

= 1.6/(4.506/SQRT(5))

= 0.794

Decision :

|T stat| < Tc, Null hypothesis is not rejected

P value :

P value = 0.4716 ( from calculator or T table)

P value > 0.05, Do not reject H0

Conclusion :

There is not enough evidence to conclude that reject the claim that the mean number of page views is the same for both​ websites, in favor of the claim of increased page visits