Question

A researcher wanted to see if students will learn more effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides twenty-four students into three groups of eight. 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 noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. SUMMARY Groups Count Sum Average Variance 8 60 constant sound random sound 7.5 4 1.43 2.863 8 32 no sound 8 27 3.38 4.84 SS df MS F P-value ANOVA Source of Variation Between Groups Within Groups Total Ferit 3.47 63.88 142.96 a. Fill in the missing information in the table (3 pts) b. What conclusion would the researcher make based on these test results? Interpret the conclusion in words using statistics from the table to support it. (2 pts) C. Calculate and interpret the effect size. (1 pt) d. After conducting her initial ANOVA test, the researcher conducted post-hoc tests. Use the results of the post-hoc testing below to compare the groups. Reference the appropriate test statistics in making your decision, as well as state the adjusted alpha and p-values you used to make your decisions. (4 pts) t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances constant random sound sound Mean 7.5 4 Variance 1.42857143 2.85714286 Observations 8 8 Hypothesized Mean 0 df 13 t Stat 4.78191036 P(T<=t) one-tail 0.00017914 t Critical one-tail 1.7709334 P(T<=t) two-tail 0.00035828 t Critical two-tail 2.16036866 Mean Variance Observations Hypothesized Mea df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail constant sound no sound 7.5 3.375 1.4285714 4.8392857 8 8 0 11 4.660252 0.0003467 1.7958848 0.0006934 2.2009852

Answer 1

	SS	df	MS	F	p-value	F-critical
Between:	78.96	2	39.48	13.0	0.000	3.47
Within:	63.88	21	3.04
Total:	142.96	23

b)

α =	0.05
Decision:	p-value<α , reject null hypothesis

c)

eta square ,effect size = SSbet/SST=   0.5526

d)

Since p value < 0.05

We can conclude that both group have different mean

Please let me know in case of any doubt.

Thanks in advance!

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