Chapter 9, Problem 20P

An example of the vertical-horizontal illusion is shown in the figure. Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this illusion, a researcher prepared an example in which both lines were exactly 10 inches long. The example was shown to individual participants who were told that the horizontal line was 10 inches long and then were asked to estimate the length of the vertical line. For a sample of $n=25$ participants, the average estimate was $M=12.2$ inches with a standard deviation of $s=1.00$ .

a. Use a one-tailed hypothesis test with $\alpha =.01$ to demonstrate that the individuals in the sample significantly overestimate the true length of the line. (Note: Accurate estimation would produce a mean of $\mu =10$ inches.)

b. Calculate the estimated d and $r^2$ , the percentage of variance accounted for, to measure the size of this effect.

c. Construct a 95% confidence interval for the population mean estimated length of the vertical line.