A market analyst wants to know if the new website he designed is showing increas

Question

A market analyst wants to know if the new website he designed is showing increased page views per visit and calculates the summary statistics in the table to the right. You may assume that the data come from a distribution that is Normally distributed. Complete parts a through d below. website 1: n1=85, y1=7.8, s1=3.1 website 2: n2=95, y1=6.8, s1=3.3 a) Find a 95% confidence interval for the mean difference, 12, in page views from the two websites b) Why is the confidence interval narrower than the one (6.19,2.99), based off of 5 randomly sampled customers for each website? c) Is 0 within the confidence interval found in part a? d.) What does the confidence interval suggest about the null hypothesis that the mean difference is 0?

Explanation / Answer

A) DF = ((3.1)^2/85 + (3.3)^2/95)^2/(((3.1)^2/85)^2/84 + ((3.3)^2/95)^2/94) = 178

With 178 degrees of freedom and 95% Confidence interval the critical value is +/- 1.9734

The confidence interval is

(y1 - y2) +/- t* * sqrt (s12/n1 + s22/n2 )

= (7.8 - 6.8) +/- 1.9734 * sqrt((3.1)^2/85 + (3.3)^2/95)

= 1 +/- 0.94

= 0.06, 1.94

B) Because for the large sample size the margin of error decreases , so that the interval becomes narrower.

C) No, 0 is not within the confidence interval.

D) As 0 doesn't lies between the interval, so the null hypothesis is rejected.

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