Question

Hayden wanted to investigate whether there was a difference in the time spent in the checkout line between two grocery stores. She went to Safeway on a Tuesday morning and recorded the time, in minutes, it took 30 customers to go through a checkout line. Then she went to Whole Foods on Tuesday afternoon and recorded the time it took 30 customers to go through a checkout line. Hayden calculated the mean number of minutes for the customers in each line. She intends to conduct a two-sample t-test for a difference in means between the two stores. Have all conditions for inference been met

Answer 1

No. The data in this study were not based on a random method. This is a key requirement for an inference to be made from the two-sample t-test.

Explanation:

1. Hayden can use the two-sample t-test (also known as the independent samples t-test)to find out if there was a difference in the time spent in the checkout time between two grocery stores and to conclude whether the difference in the average checkout time between the two stores is really significant or if the difference is due to a random chance. There are three conditions to be met when using the two-sample t-test.

2. The first condition is that the sampling method must be random. This requirement was not met in this study. Each customer from each store should have an equal chance of being selected for the study. This was not achieved.

3. The distributions of the sample data are approximately normal. This is achieved with a large sample size of 30 customers selected for each study.

4. The last but not the least condition is the independence of the sample data. Sample data here is independent for both samples.