Question

An experiment on memory was performed, in which 16 subjects were randomly assigned to one of two groups, called "Sentences" or "Intentional". Each subject was given a list of 50 words. Subjects in the "Sentences" group were told to form multiple sentences, each using at least two words from the list, and to keep forming sentences until all the words were used at least once. Subjects in the "Intentional" group were told to spend five minutes memorizing as many of the 50 words as possible. Subjects from both groups were then asked to write down as many words from their lists as they could recall. The data are in the table below.

Number of words recalled

"Sentences" group	29	26	36	28	36	31	32	28
"Intentional" group	30	40	32	29	33	29	32	32

IMPORTANT: to format this data correctly, you need to think about what your two variables are (they are not 'Sentences' and 'Intentional'). You may want to look at how the deflategate data are formatted if you have trouble figuring this out.

We are interested in determining if there is a significant difference in the average number of words recalled for subjects in the "sentences" group vs. subjects in the "intentional" group, using α = 0.05

a. The appropriate null/alternative hypothesis pair for this study is:

1. H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional ≠ 0

2. Ho: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional < 0

3. H₀: μ_d = 0 ; H_A: μ_d ≠ 0

4. H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional > 0

5. H₀: μ_d = 0 ; H_A: μ_d > 0

6. H₀: μ_d = 0 ; H_A: μ_d < 0

b. Enter the values for the following statistics:

x_sentences =  
s_sentences =  
x_intentional =  
s_intentional =  
(x_sentences - x_intentional) =  
standard error of (x_sentences - x_intentional) =
test statistic: t =  
p-value =  

c. Report the 95% confidence interval JMP gives for μ_sentences - μ_intentional

Lower bound =  
Upper bound =  

d. From these results, our statistical conclusion should be:
(You have two attempts at this question.)

1. The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and zero is inside the confidence interval

2. The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and zero is outside the confidence interval    The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and -1.375 is inside the confidence interval

3. The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and -1.375 is outside the confidence interval

4. The means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and zero is inside the confidence interval

5. The means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and zero is outside the confidence interval

6. The means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and -1.375 is inside the confidence interval

7. The means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and -1.375 is outside the confidence interval

Answer 1

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Coni Scanned with CamScanner

R Console > sentences-C (33,35, 30,28,33,24,27,31) > intentional-c (36,38,36, 32,33,36,29,35) > t.test (sentences,intentional) Welch Two Sample t-test data: sentences and intentional t 2.5903, df13.284, p-value0.0221 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -7.7868752 -0.7131248 sample estimates: mean of x mean of y 34.375 30.125 2 > mean (sentences) [1 30.125 > sd (sentences) [1] 3.642507 > mean (intentional) [11 34.375 > sd (intentional) [1] 2.875388