Question

The paper "If It's Hard to Read, It's Hard to Do" (Psychological Science [2008]: \(986-988\) ) described an interesting study of how people perceive the effort required to do certain tasks. Each of 20 students was randomly assigned to one of two groups. One group was given instructions for an exercise routine that were printed in an easy-to-read font (Arial). The other group received the same set of instructions but printed in a font that is considered difficult to read the time (in minutes) they thought it would take to complete the exercise routine. Summary statistics follow. The authors of the paper used these data to carry out a twosample \(t\) test and concluded at the 0.10 significance level that the mean estimated time to complete the exercise routine is significantly lower when the instructions are printed in an easy-to-read font than when printed in a font that is difficult to read. Discuss the appropriateness of using a twosample \(t\) test in this situation.

Short answer

The two-sample t-test can help in understanding how different fonts affect students' perception of exercise time, however, its presumptions about equal variances and normal distributions can't be confirmed from the current information, thus its outcome, despite being significant, should be approached cautiously.

Step-by-step solution

Understand the problem

A two-sample t-test is used to compare the means of two separate populations. In this case, the two-population are students who were given instructions in an easy-to-read font and those given instructions in a difficult-to-read font. The parameter of interest is the mean estimated time to complete an exercise routine.

Verify t-test assumptions

In order to use a t-test, certain assumptions must hold: 1. The samples are independently and randomly drawn. This assumption is met since students are randomly assigned to one of the two groups. 2. The populations from which the samples were drawn are normally distributed. There's no practical way to validate this assumption from the information given, but the t-test is known to be robust to violations of this assumption especially as the sample size grows. 3. The populations have the same variance. We can't validate this from the information given.

Discuss appropriateness of t-test

The two-sample t-test appears to be a reasonable approach for answering the question of whether font readability affects the perceived time to complete the exercise. However, the conclusions drawn can only be as reliable as the assumptions made. While the sampling process appears to be random and independent, we have no information about whether the variance is the same for both populations or whether the populations are normally distributed. Therefore, while the two-sample t-test might give some insight, its conclusions should be considered carefully.