Question

Price Differentiating E-commerce websites "alter results depending on whether consumers use smartphones or particular web browsers," 34 reports a new study. The researchers created clean accounts without cookies or browser history and then searched for specific items at different websites using different devices and browsers. On one travel site, for example, prices given for hotels were cheaper when using Safari on an iPhone than when using Chrome on an Android. At Home Depot, the average price of 20 items when searching from a smartphone was \(\$ 230,\) while the average price when searching from a desktop was \(\$ 120 .\) For the Home Depot data: (a) Give notation for the two mean prices given, using subscripts to distinguish them. (b) Find the difference in means, and give notation for the result.

Short answer

The notation for the mean prices for searching from a smartphone and desktop are \( M_1 \) and \( M_2 \) respectively. The difference in means, denoted by \( D \), is $110.

Step-by-step solution

Define the notation for the mean prices

Given two mean prices, these can be distinguished using subscripts. Let \( M_1 \) denote the mean price when searching from a smartphone which is $230, and let \( M_2 \) denote the mean price when searching from a desktop which is $120.

Compute the difference in means

To find the difference in means, subtract the mean price when searching from a desktop (\( M_2 \)) from the mean price when searching from a smartphone (\( M_1 \)). This is executed by the following computation: \( M_1 - M_2 = 230 - 120 = 110 \). So, the difference in means is $110.

Define the notation for the difference in means

The difference in means can be represented using notation too. Let's denote the difference as \( D \), so \( D = M_1 - M_2 \). Hence, the notation for the difference is \( D \).