Question

1. A researcher wants to test whether color can influence recall of words in a list. To test this, the researcher displays 20 words on a computer screen. Ten words are in color, and 10 words are in black. All words are presented on a white background. Participants are given 1 minute to view the list, and then the list is taken away and participants are allowed 1 additional minute to write down as many words as they can recall. The researcher records the number of colored versus black words accurately recalled. The results are in color.txt. Conduct a related samples t-test to test whether the color of words in the list influenced recall. Use R to a two-tailed test, alpha = .05.

Participant   Color   Black
1   7   4
2   8   4
3   4   6
4   6   4
5   4   6
6   8   2
7   6   3
8   7   3
9   5   6
10   6   9
11   4   5
12   6   7
13   5   5
14   8   3
15   9   0
16   10   0
17   6   8
18   4   6
19   2   6
20   8   4
21   6   2
22   4   1

a. Write the null hypothesis in symbols and words

b. Write the alternative hypothesis in symbols and words

c. By hand, calculate the degrees of freedom. Show calculation.

d. Use the t-test function in R to obtain the test statistic and p-value

e. Make a decision about the null using the p-value approach

f. Write the conclusion in APA style

g. Using R, compute and report the 95% CI.

h. Interpret the 95% CI.

i. Using the CI, make a decision about the null hypothesis. Be sure to explain your reasoning.

j. Does this agree with your decision from part (e)?

Answer 1

color=c(7,8,4,6,4,8,6,7,5,6,4,6,5,8,9,10,6,4,2,8,6,4)
black=c(4,4,6,4,6,2,3,3,6,9,5,7,5,3,0,0,8,6,6,4,2,1)
t.test(color,black, var.equal=FALSE, paired=TRUE)

Output:

Paired t-test

data: color and black
t = 2.1576, df = 21, p-value = 0.04269
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.0641128 3.4813417
sample estimates:
mean of the differences
1.772727

Value of test statistic=2.1576, p-value=0.04269

e. p-value<0.05 so we reject H₀ at 0.05 level of significance.

f. Color can influence recall of words in a list.

g. 95 percent confidence interval:
(0.0641128, 3.4813417)

h. We are 95% confident that the mean difference between no. of color words recall and no. of black words recall lies between 0.0641128 and 3.4813417.

i. Since the C.I. does not contain zero hence we reject H₀.

j. Yes.