Question

A psychologist researching memory prepares a list of 40 noun pairs (e.g., dog/bicycle; grass/door). He then recruits two groups of subjects. Group 1 is given 5 minutes with the list and is instructed to create a mental image for each pair (for example, to imagine a dog riding a bicycle). Group 2 is also given 5 minutes, but they are told to memorize the pairs. Later each group is given a memory test in which they are given the first word of the pair and are asked to recall the second word. The number of words correctly recalled is reported below. Based on these data, can the researcher conclude that mental images affected memory? Answer using the 7 steps of hypothesis testing, setting alpha at .01. You are additionally given the following information: M_I = 26, M_NI = 18, s_I = 4.71, s_NI = 4.22, SE_{MI – NI} = 2

            Group 1 (Images)                               Group 2 (No images)

            19                                                                    23

            20                                                                    22

            24                                                                    15

            30                                                                    16

            31                                                                    18

            32                                                                    12

            30                                                                    16

            27                                                                    19

            22                                                                    14

            25                                                                    25

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 >   0                 
                          
Level of Significance ,    α =    0.01                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   26.00                  
standard deviation of sample 1,   s1 =    4.71                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   18.00                  
standard deviation of sample 2,   s2 =    4.22                  
size of sample 2,    n2=   10                  
                          
difference in sample means =    x̅1-x̅2 =    26.0000   -   18.0   =   8.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    0.8190                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.3663                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   8.0000   -   0   ) /    0.37   =   21.842
                          
Degree of freedom, DF=   n1+n2-2 =    18                  
with crtical value approch

t-critical value , t* =        2.5524   (excel function: =t.inv(α,df)              
Decision:   | t-stat | > | critical value |, so, Reject Ho            

.....

with p value approch
p-value =        0.000000   [excel function: =T.DIST.RT(t stat,df) ]             
decision:     p-value <α , Reject null hypothesis     

conclusion : there is enough evidence to conclude that  mental images affected memory

.......

Please revert back in case of any doubt.

Please upvote. Thanks in advance.