Chapter 12, Problem 27SE

Reading Colored Paper (Example 4) Some people believe that it is easier to read words printed on colored paper than words printed on white paper. To test this theory, statistics student Paula Smith collected data. Subjects were timed as they read a pas-sage printed in black ink on a sheet of salmon-colored paper and as they read the same passage printed with black ink on a sheet of white paper. Each person was randomly assigned to read material printed on either the white or the salmon paper first. The times in seconds are given in the table. We are assuming that smaller times (faster reading) imply that the reading is easier. Assume that these are a random sample of times and that the distribution of times is sufficiently close to Normal for $t$ -tests.

a. Compare the sample means. Does your result fit the theory given?

b. Use a two-sample $t$ -test; report the $t$ -statistic and $p$ -value, and report whether you can reject the null hypothesis of no difference in times at the 0.05 level.

c. Use a paired $t$ -test; report the $t$ -statistic and $p$ -value, and report whether you can reject the null hypothesis of no difference in times at the 0.05 level.

d. Which is the appropriate test for this data set?

e. Why is it essential that the researchers randomly assign the order so that some of the people read material on the salmon-colored paper first and some read material on the white paper first?