Question

Researchers conducted a study to investigate the effects of color on cognitive tasks. Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below:

           

Red Background: n = 35	15.89	s = 5.90
Blue Background: n = 36	12.31	s = 5.48

1. Use a 0.05 significance level to test the claim that the samples are from populations with the same mean.
2. Does the background color appear to have an effect on word recall scores? If so, which color appears to be associated with higher word memory recall scores?
3. What are the null and alternative hypotheses?
4. What is the value of significance level?
5. Is the test two-tailed, left-tailed or right-tailed?
6. What is the test statistic and what is its distribution?
7. What is the value of the test statistic?
8. What is the P-value?
9. What is (are) the critical value(s)?
10. How would you state a conclusion that addresses the original claim?

Answer 1

(A)

H0:Null Hypothesis: (The samples are from populations with the same mean) (Claim)

HA: Alternative Hypothesis: (The samples are not from populations with the same mean)

n1 = 35

1 = 15.89

s1 = 5.90

n2 = 36

2 = 12.31

s2 = 5.48

= 0.05

Pooled Standard Deviation is given by:

Test Statistic is gieven by:

df = 35 +36 - 2 = 69

From Table, critical values of t = 1.995

Sincecalculated value of t = 2.65 is greater than critical value of t = 1.995, the difference is significant. Reject null hypothesis.

By Technology,

p - value = 0.0100

Since p - value = 0.0100 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support theclaim that the samples are from populations with the same mean.

(B)

The background color appears to have an effect on word recall scores. Red color appears to be associated with higher word memory recall scores.

(C)

H0:Null Hypothesis: (The samples are from populations with the same mean) (Claim)

HA: Alternative Hypothesis: (The samples are not from populations with the same mean)

(D)

Significance level = = 0.05

(E)

The test is two tailed.

(F)

Test statstic is t. Its distribution is t distribution with 69 degrees offreedom.

(G)

The value of the test statistic = 2.65

(H)

The P - value = 0.0100

(I)

The critical values are: 1.995

(j)

The data do not support theclaim that the samples are from populations with the same mean.