Question

A relationships researcher (who double majored in English and Psychology as an undergraduate) recalled a well-known phrase from a poem by Alfred, Lord Tenyson, that in the spring, a young person’s fancy turns to thoughts of love. She specifically wanted to test the hypothesis that students are more likely to be distracted by thoughts of romance in the spring than in the fall. She selected a random sample of 12 college students. She measured distractedness via a reaction time test on a computer, where the participants were to press the space bar as soon as they find a target stimulus on the screen that was hidden in a field of distractor stimuli. The software recorded the reaction time elapsed in milliseconds—where longer reaction times indicate more distraction. The researcher held the time in the semester constant by running the participants in the experiment during midterm exams in both the fall and the spring semesters. Was Lord Tenyson’s poem correct?    

Student	Fall	Spring	Student	Fall	Spring
1	539	715	7	336	734
2	548	710	8	541	706
3	534	776	9	543	717
4	433	357	10	646	738
5	548	734	11	556	526
6	514	727	12	549	640

a. identify the statistical test

b. State the null and alternative hypotheses.

c. What is the critical value of the test statistic? What is the decision rule for rejecting the null hypothesis?

CV:         _________________________           Reject H₀ if t _____________________

d. Paste in your SPSS output here. Circle the means, standard error, and observed value of t on the output.

    

Show your work for t observed (using formula and plugging in appropriate numbers from output) and eta² here:

t_obs=

eta² =

e. Write out an APA Style conclusion about the research project, using the context of the study in your answer.

Answer 1

a. identify the statistical test

The statistical test is a Paired t-test.

b. State the null and alternative hypotheses.

The hypothesis being tested is:

The null hypotheses, H₀: µ₁ = µ₂

Students are equally likely to be distracted by thoughts of romance in the spring and in the fall

The alternative hypotheses, H_a: µ₁ < µ₂

Students are more likely to be distracted by thoughts of romance in the spring than in the fall

c. What is the critical value of the test statistic? What is the decision rule for rejecting the null hypothesis?

CV: 1.80 Reject H₀ if t >1.80

d. Paste in your SPSS output here. Circle the means, standard error, and observed value of t on the output.

523.917	mean Fall
673.333	mean Spring
-149.417	mean difference (Fall - Spring)
123.278	std. dev.
35.587	std. error
12	n
11	df
1.796	t Critical one-tail
-4.199	t
.0007	p-value (one-tailed, lower)

Show your work for t observed (using formula and plugging in appropriate numbers from output) and eta² here:

t_obs= -4.199

eta² = 35.587

e. Write out an APA Style conclusion about the research project, using the context of the study in your answer.

Since |t_obs| > t_cric, we can reject the null hypothesis.

Therefore, we can conclude that the students are more likely to be distracted by thoughts of romance in the spring than in the fall.