Using the standard error of the differnece of means to answer this question in a
ID: 3229781 • Letter: U
Question
Using the standard error of the differnece of means to answer this question in a detailed step-by-step breakdown using the formula the proper formulas to find the standard error of the difference of means as well as find the degree of freedom, whether its two or one tailed test, critical value and caluclated values to either retain or reject the null: (do not use excel or spss)
A professor conducting research on memory. She shows her subjects (volunteers from her intro class) a list of words on the computer, with some of the words being food items and the rest of the words being completely unrelated. She then gives each subject 30 seconds to recall as many words from the list as possible, with her theory being that the subjects will be able to remember the food-related words better than the unrelated words. With the following results, test the null hypothesis of no significant difference between the number of food-related and nonfood-related words that the subjects could remember. What do the results indicate?
Food-Related
Nonfood-Related
N1 = 11
N2 = 11
x1= 5.54
x2= 2.91
S1 = 1.73
S2 = 1.93
Food-Related
Nonfood-Related
N1 = 11
N2 = 11
x1= 5.54
x2= 2.91
S1 = 1.73
S2 = 1.93
Explanation / Answer
Test statistic t= (xbar1-xbar2)/sqrt((1/n1+1/n2)*((n1-1)*s12+(n2-1)*s22)/(n1+n2-2)))
=(5.54-2.91)/sqrt((1/11+1/11)*(10*1.73*1.73+10*1.93*1.93)/(11+11-2))
=3.3654
degree of freedom=n1+n2-2=11+11-2=20
p-value=0.003
As p-value,0.05, we conclude that there is significant difference between the number of food-related and nonfood-related words that the subjects could remember.
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