Question

Matched pairs or independent/separate samples? For each of the prompts below, decide whether the parameter of interest is a mean difference (matched pairs, μ_d) or a difference in means (independent samples, μ₁- μ₂). Students want to know if it matters where they have their cell phone screen repaired. A sample of eight cell phones with broken screens was obtained. For each phone, an estimate for the screen repair in U.S. dollars ($) was obtained from a local store, where the phone would be dropped off and picked up, and from an on-line merchant, where the phone needs to be shipped to a national chain and shipped back. Your goal is determining if, on average, the estimate in dollars for the total repair from the on-line merchant is more (possibly because of the added cost of shipping) than the estimate from a local store. Is this a matched pairs (μ) or independent/separate samples (μ₁- μ₂) scenario?

Answer 1

For cell phones receiving estimates from both a local store and an online merchant, the situation is a matched pairs scenario, focusing on the mean difference in cost using a matched pairs t-test.

Step-by-step explanation:

The scenario described involves comparing the cost of screen repairs for the same set of cell phones by two different vendors, a local store and an online merchant. Since the cost estimates are obtained for the identical set of cell phones, this would be a matched pairs situation.

Each cell phone serves as its own control, and the pairing is based on each phone receiving two types of estimates. Therefore, the parameter of interest is a mean difference (μd) and not a difference in means (μ1 - μ2).

In matched pairs designs, the main analysis involves the differences between the matched pairs. In this case, you would calculate the difference in cost estimates for each phone (local estimate minus online estimate) and treat these differences as a single sample.

A t-test for matched pairs would then be used to determine if there is a statistically significant difference in the average cost of screen repairs between local stores and online merchants.