Question

A cognitive Psychologist is interested to see if the color of ink when reading affects the speed at which a person recognizes words. Based on published studies, it is known that on average the general population takes µ = 880 milliseconds to recognize common words like apple, but the standard deviation for the population varies across these studies, so we do not know the population deviation. A psychologist presents a sample of n = 16 participants with common words that are names of colors. However, the color names are printed in a color of ink different from the word itself. That is, the word red is printed in blue ink, or green is printed in brown etc. Mean recognition time for these words was M = 910 msec, with a sample standard deviation of SD = 20 msec.

A. What is the type of statistical test you would use in this study?

B. Why do you use this type of statistical test?

C. What is the I.V.?

D. What is the D.V.?

Use the four steps of hypothesis testing.

E.. Step 1:

F. Step 2:

G. Step 3:

H. Step 4:

State your conclusion about the null hypothesis:

Answer 1

a) One would use the t test for mean for this study.

b) For the given population we only know the mean and not the variance of the population. Also the sample is very sample with only 16 units. Hence, t test is the best statistical test to test the significance of the mean.

c) The independent variable is the colour of ink.

d) The dependent variable is the time taken to read the words.

e) The hypothesis are:

H0: Ink color does not affect the mean time to read common words; mu = 880ms

H1: Ink color increases the mean time to read common words; mu > 880ms

The test statistic under the null hypothesis is:

t = 6

The corresponding p value is 0.0000122 for 15 degrees of freedom

Since, the p-value is much less tha 0.05 we reject the null hypothesis at 5% level of significance and conclude that the ink colour increases the mean time to read the common words.