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	23	31	32	27	27	31	27	31
"Intentional" group	33	33	33	34	28	36	34	30

Enter this data into JMP in "long form" (e.g. each column should be a variable and each row should be an observation).
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. Use JMP to answer the questions below, and round all answers to three decimal places.

a. The appropriate null/alternative hypothesis pair for this study is:
(you have two attempts at this question)

H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional > 0Ho: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional < 0    H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional ≠ 0H₀: μ_d = 0 ; H_A: μ_d < 0H₀: μ_d = 0 ; H_A: μ_d ≠ 0H₀: 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) =  (you have to use 'Analyze / Fit Y by X' to get JMP to calculate this)
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.)

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

Answer 1

a)

H₀: μ_sentences - μ_intentional = 0

H_A: μ_sentences - μ_intentional ≠ 0

b)

Equal variances assumed for the analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
"Sentences" group	8	28.63	3.11	1.1
"Intentional" group	8	32.63	2.50	0.89

Estimation for Difference

Difference	Pooled StDev	95% CI for Difference
-4.00	2.83	(-7.03, -0.97)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-2.83	14	0.013

x_sentences = 28.63
s_sentences = 3.11
x_intentional = 32.63
s_intentional = 2.50
(x_sentences - x_intentional) = -4.0
standard error of (x_sentences - x_intentional) = 1.428
test statistic: t = -2.83
p-value =   0.013

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

Lower bound = -7.03
Upper bound =   -0.97

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