Question

My friend, Bob, believes that his supermarket's prices are lower than mine. We construct a list of identical items and purchase them at our respective stores every week for two months. Then Bob wants to know if his hypothesis is supported.

Answer 1

GIVEN:

Bob believes his supermarket's prices are lower than his friend.

A list of identical items are constructed and purchased at their respective stores every week for two months.

TO FIND:

Bob wants to know if his hypothesis is supported.

SOLUTION:

From the claim "Bob believes his supermarket's prices are lower than his friend",

Bob has a directional hypothesis. A directional hypothesis is a one-tailed hypothesis that states the direction of the difference or relationship. Since the claim is that "Bob believes his supermarket's prices are lower than his friend", it is a left tailed directional hypothesis.

Since a list of identical items are constructed and purchased at their respective stores every week for two months, it is considered as matched pair sample since same set of items were purchased for two different months.

Thus matched-pair t-test (or paired t-test or paired samples t-test or dependent t-test) is used when the data from the two groups can be presented in pairs, for example where the same people are being measured in before-and-after comparison or when the group is given two different tests at different times.

Thus Bob should do a matched t test to test the hypothesis "Bob believes his supermarket's prices are lower than his friend" using matched pair sample of items purchased for two different months.

Thus Bob has a directional hypothesis and should do a matched t test. Hence Bob's hypothesis is supported.