The paper "If It's Hard to Read, It's Hard to Do"+ 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 (Brush). After reading the instructions, subjects estimated the time (in minutes) they thought it would take to complete the exercise routine. Summary statistics are given below. Difficult font 10 Easy font n 10 x 8.23 5.61 15.10 9.28 The authors of the paper used these data to carry out a two-sample t test, and concluded that at the 0.10 significance level, there was convincing evidence that the mean estimated time to complete the exercise routine was less when the instructions were printed in an easy-to-read font than when printed in a difficult-to-read font. Discuss the appropriateness of using a two-sample t test in this situation. The treatment groups were small, so in order to use the two-sample t test it is necessary to assume that the population distributions of estimated times for each group are normal. However, in both samples zero is about 3 standard deviations below the mean. If we assume that the populations have means and standard deviations equal to the sample means and standard deviations, this would imply that a significant proportion of people in each population have negative estimated times. Since this is impossible, the populations are unlikely to be approximately normally distributed and the two-sample t test is not appropriate. The treatment groups were small, so in order to use the two-sample t test it is necessary to assume that the population distributions of estimated times for each group are normal. However, in both samples zero is about 3 standard deviations below the mean. If we assume that the populations have means and standard deviations equal to the sample means and standard deviations, this would imply that almost all of people in each population have positive estimated times. Since we can only have positive times, this supports the assumption that the populations are approximately normally distributed and the two-sample t test is appropriate. The treatment groups were small, so in order to use the two-sample t test it is necessary to assume that the population distributions of estimated times for each group are normal. However, in both samples zero is about 1.5 standard deviations below the mean. If we assume that the populations have means and standard deviations equal to the sample means and standard deviations, this would imply that a significant proportion of people in each population have negative estimated times. Since this is impossible, the populations are unlikely to be approximately normally distributed and the two-sample t test is not appropriate. The treatment groups were small, so in order to use the two-sample t test it is necessary to assume that the population distributions of estimated times for each group are normal. However, in both samples zero is about 1.5 standard deviations below the mean. If we assume that the populations have means and standard deviations equal to the sample means and standard deviations, this would imply that almost all of people in each population have positive estimated times. Since we can only have positive times, this supports the assumption that the populations are approximately normally distributed and the two-sample t test is appropriate.