Question

Name: Please complete the following problems using SPSS and Excel for graphs. Interpretal results at the.os significance level and round to boro decimal places. Record your responses in the aces provided and make sure you do not miss any questions. Make sure to include statistical notation when appropriate and double check your data entry! 1 A researcher wants to evaluate the learning ability of college students with various background sounds during learning. She randomly divides 21 participants into three groups. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with background sound that changes volume randomly. Those in group 3 study with no sound at all. After studying, all students take a 10-point multiple choice test about the material. Their scores follow Constant sound 7 No sound 5 6 4 Random sound 5 5 3 4 4 6 7 9 8 6 6 6 B 7 6 9 2 A. What statistical test should you perform? Be as specific as possible. (7 points) B. What is the overall result of the statistical analysis (hint: think "First sentence")? Include statistical notation. (9 points) C. is the constant sound group significantly different from the random sound group? Describe the relationship and include statistical notation. (9 points) D. is the constant sound group significantly different from the no sound group? Describe the relationship and include statistical notation. (9 points) E. is the random sound group significantly different from the no sound group? Describe the relationship and include statistical notation. (9 points) F. Write a sentence in "plain English" that describes the results of the experiment. 7 points) Bonus: Graph your results (include axis titles, chart title, and SEM error bars). 5 points)

Answer 1

(a) One-Way ANOVA test

(b) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

	Mean	n	Std. Dev
	6.6	7	1.62	Group 1
	4.1	7	1.35	Group 2
	6.9	7	1.35	Group 3
	5.9	21	1.85	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	31.14	2	15.571	7.49	.0043
Error	37.43	18	2.079
Total	68.57	20

The p-value is 0.0043.

Since the p-value (0.0043) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that not all means are equal.

(c) There is a significant difference between the constant sound group and the random sound. (M = 3.15, p < 0.05)

(d) There is no significant difference between the constant sound group and the no sound group. (M = 0.37, p > 0.05)

(e) There is a significant difference between the no sound group and the random sound. (M = 3.52, p < 0.05)

(f) There is a significant difference in the learning ability of college students with various background sounds.

Tukey simultaneous comparison t-values (d.f. = 18)
		Group 2	Group 1	Group 3
		4.1	6.6	6.9
Group 2	4.1
Group 1	6.6	3.15
Group 3	6.9	3.52	0.37
critical values for experimentwise error rate:
		0.05	2.55
		0.01	3.32

Graph:

Interval Plot of C1, C2, ... 95% CI for the Mean 8 7 Data 5 4 3 C1 C2 C3 The pooled standard deviation is used to calculate the intervals.