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. Assume that the data come from a distribution that is Normally distributed. The data is shown in the table to the right. Complete parts a through c below. Website 1: n1= 70 y1= 7.8 s1= 5.1 Website 2: n2= 95 y2= 7.2 s1= 5.8

a) Test the null hypothesis at alpha = 0.05 using the pooled t-test.

Assume that the new website is website 1 and the old website is website 2.

Choose the null and alternative hypotheses below.

A. Upper H 0 : mu 1 - mu 2 = 0

Upper H A : mu 1 - mu 2 < 0

B. Upper H 0 : mu 1 = mu 2 not equals 0

Upper H Subscript Upper A : mu 1 not equals mu 2 = 0

C. Upper H 0 : mu 1 - mu 2 = 0

Upper H Subscript Upper A : mu 1 - mu 2 not equals 0

D. Upper H 0: mu 1 - mu 2 = 0

Upper H Subscript Upper A : mu 1 - mu 2 > 0

Calculate the test statistic. Let the difference of the sample means be y overbar 1 - y overbar 2.

t = .....

(Round to three decimal places as needed.)

Calculate the P-value.

P-value= ......

(Round to four decimal places as needed.)

State the conclusion.

Choose the correct answer below.

A. Fail to reject Upper H 0. There is not sufficient evidence that the difference in the mean number of page views is greater than 0.

B. Fail to reject Upper H 0. There is sufficient evidence that the difference in the mean number of page views is greater than 0.

C. Reject Upper H 0. There is sufficient evidence that the difference in the mean number of page views is greater than 0.

D. Reject Upper H 0. There is not sufficient evidence that the difference in the mean number of page views is greater than 0.

b) Find a 95% confidence interval for the mean difference in page views from the two websites using the pooled degrees of freedom.

(.... , ....)

(Round to two decimal places as needed.)

c) The confidence interval for the unpooled variance is (1.08 , 2.28 ). Are your answers different from the interval where the variance is not pooled? Explain briefly why or why not.

A. The confidence intervals are significantly different because the standard deviations for the two websites are fairly close.

B. The confidence intervals are close because the standard deviations for the two websites are fairly close.

C. The confidence intervals are significantly different because the standard deviations for the two websites are significantly different.

D. The confidence intervals are close because the standard deviations for the two websites are significantly different.

Answer 1

a) option D is correct

from above test statistic t=0.691

p value =0.2453 ( please try 0.2454 if this comes wrong)

A. Fail to reject Upper H 0. There is not sufficient evidence that the difference in the mean number of page views is greater than 0.

b)

for 95 % CI & 163 df value of t=				=	1.9750
margin of error E=t*std error                            =					1.7156
lower confidence bound=mean difference-margin of error =					-1.12
Upper confidence bound=mean differnce +margin of error=					2.32

95% confidence interval for the mean difference=-1.12 ; 2.32

c)

B. The confidence intervals are close because the standard deviations for the two websites are fairly close.