Question

1. Participants saw a series of words on a computer screen. Each time, a word (either relating to a positive emotion or a negative emotion) was presented on a screen for 1500ms. Researchers asked participants to press the “A” key as quickly as possibly if they saw a positive word and the “L” key if they saw a negative word. The response is reaction time in milliseconds (i.e., how long it took the subject to make a response). Use an appropriate test statistical method to answer the question: Did the reaction time differ between the two types of words?

Subjects	Positive	Negative
1	500	490
2	540	540
3	340	350
4	540	580
5	480	500
6	465	490
7	400	450
8	440	450
9	430	420
10	435	450

Please resolve the following questions:

1. Identify the independent variable and its associated levels, as well as the dependent variable. (12 pts)
2. Identify the statistical test to be used. (4 pts)
3. State the null and alternative hypothesis. (6 pts)
4. Determine the critical value(s). (4 pts)
5. Calculate the value of your test statistic from the data. (24 pts)
6. Draw a distribution showing your critical regions and test statistic. (7 pts)
7. Make a statistical decision for the hypotheses. (6 pts)
8. Interpret the results and answer/validate the research question - Did the reaction time differ between the two types of words? (12 pts)

Answer 1

The independent variable is the two types of words and its associated level is 2. The dependent variable is the reaction time.

The statistical test to be used is the Paired t-test.

The hypothesis being tested is:

H0: µd = 0

Ha: µd ≠ 0

Subjects	Positive	Negative	Difference
1	500	490	10
2	540	540	0
3	340	350	-10
4	540	580	-40
5	480	500	-20
6	465	490	-25
7	400	450	-50
8	440	450	-10
9	430	420	10
10	435	450	-15
		457.000	mean Positive
		472.000	mean Negative
		-15.000	mean difference (Positive - Negative)
		19.720	std. dev.
		6.236	std. error
		10	n
		9	df
		2.262	critical t
		-2.405	t
		.0395	p-value (two-tailed)

The critical value(s) are -2.262 and 2.262.

The value of the test statistic is -2.405.

The distribution showing your critical regions and the test statistic is:

The p-value is 0.0395.

Since the p-value (0.0395) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the reaction time differs between the two types of words.

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