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. A customer is randomly sent to one of two different websites, offering the same products, but with different designs Here are the page views from five randomly chosen customers from each website: a) Find the sample mean page views for each website. b) Find the estimated difference of the sample mean page views of the two websites. c) Find the sample variances for each website. d) Find the sample standard deviations for each website. e) Find the standard error of the difference of the sample means.

Explanation / Answer

Solution

Back-up Theory

Sample Mean and Sample Standard Deviation

Let x1, x2, x3,       , xn be a sample of n observations. Then,

Sample mean, Xbar = (1/n){sum of xi, i = 1, 2, ……., n} …………………………….(1)

Sample variance, V(X) = s2(X) = {1/(n - 1)}{sum of (xi – Xbar)2, i = 1, 2, ……., n}……. ….(2)

(2) can also be expressed as s2(X) = {1/(n - 1)}{sumxi2 - n(Xbar)2}…………………(3)

Sample standard deviation, SD(X) = s(X) = square root of V(X) …………………………….(4)

Now, to work out solution,

Let X = page views of website A and Y = = page views of website B,

Part (a)

[vide (1) under Back-up Theory], Sample mean page views for

website A = Xbar = 36/5 = 7.2 and website B = Ybar = 25/5 = 5 ANSWER

Part (b)

Estimated difference between sample mean page views = 7.2 – 5 = 2.2 ANSWER

Part (c)

[vide (2) under Back-up Theory], sample variance for

website A = V(X) = 91.4/4 = 22.85 and website B = V(Y) = 46.4/4 = 11.5 ANSWER

Part (d)

[vide (4) under Back-up Theory], sample standard deviation for

website A = SD(X) = 22.85 = 4.78 and website B = SD(Y) = 11.5 = 3.39 ANSWER

Part (e)

Standard error for the difference between two sample means = s(2/n), where

s2 = {s2(X) + s2(Y)}/2 = (22.85 + 11.5)/2 = 17.175 and s = 17.175 = 4,144

Standard error for the difference between two sample means = 4.144(2/4) = 4.144x0.707

= 2.93 ANSWER

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