Question

Although the two lines are exactly the same length, the vertical line appears to be much longer. This is a "robust" effect, meaning that even if you know that the lines are the same length and measure them yourself, the vertical one will still look longer.

A researcher wants to know if this effect can be overcome with extensive training to correctly see the length of the lines. On average, the population estimate is that vertical lines are 20% longer--so for example, a 10" line will be estimated as 12".

The researcher recruits a sample of n = 25 participants, and trains them to try to see the lines accurately for four weeks. After training, the average estimate was for the vertical line to be 10% longer, with a standard deviation of s = 15%.

Use a two-tailed hypothesis test with alpha = 0.05 to determine whether the participants in this experiment significantly reduced how much they over-estimate the line lengths. (Hint: compare the population µ = 20% to the sample M = 10% with s = 15%.)

A. what is the estimated standard error of the mean, s_m?

B. what is the t-stat for this sample?

C.  how many degrees of freedom are there?

D. what is the critical t-stat? Assume an alpha = 0.01 two-tailed test.

E. So, what's the answer? Did the training significantly reduce how much the participants over-estimate the length?

F. What is Cohen's d effect size for this experiment?

G.

What is the 95% CI for how much the participants over-estimate the length? That is, what is the 95% range around the mean estimate of M = 10%?

Answer 1

A.

s_m = s/

= 15/5

= 3

B.

t =

= (10-20)/3

= -3.333

C.

df = n-1

= 24

D.

Critical t-value = 2.797

E.

Since 3.333 > 2.797 i.e. we can reject null hypothesis and hence we can say that training significantly reduced by how much the participants over-estimate the length.

F.

d =

= (10-20)/15

= -0.667

G.

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