In the vertical-horizontal line illusion, the two lines are exactly the same len
ID: 3059728 • Letter: I
Question
In the vertical-horizontal line illusion, the two lines are exactly the same length, but 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.
39. For a one-tailed test with = 0.01, what is the null hypothesis?
40. Calculate df for this test.
41. What is the critical value for t?
42. Calculate estimated standard error.
43. Calculate t.
44. Based on the t-statistic you calculated, what is your conclusion (accept or reject H0)?
45. Calculate the estimated Cohen’s d.
46. Calculate r 2 .
Explanation / Answer
39. The Null hypothesis is: The average estimate of the vertical line is 10 inches
40. DF, degrees of freedom = 25-1 = 24
41. Critical value of t, t24,0.01 can be calculated from a standard t-table with 24 degrees of freedom or using MS Escel
t24,0.01 = 2.4922
42. Standard Error = /n = 1 / 25 =1/5 = 0.2
43. t = (12.2-10) / 0.2 = 11
44. Since t > tcritical, we reject the Null Hypothesis
45. Cohen's d = 2.2/1 = 2.20
46. r2 = 121/145 = 0.8345