in a study of memory recal 5 people were given 10 minutes to memorize a list of

Question

in a study of memory recal 5 people were given 10 minutes to memorize a list of 20 words. each was asked as many of the words as he or she could remember both 1 hour ans 24v hours later. the result are as follows

subject 1 hour later 24 hours later

1 14 12

2 18 15

3 11 9

4 13 12

5 12 12

is there evidence to bsuggest that the mean number of words recaled after 1 hourv exceeds the mean recall after 24 hours assme we want to use a 0.10 significance level to test the claim

a) identify null hypothesis and alternative hypothesis b) determine the test statistic show all workc) the p-value for this test show all work d) is there sufficient evidence to support the claim that the mean numbrer of words recalled after 1 hour exceeds the mean recal after 24 hours justify your conclusion

1   

Explanation / Answer

Set Up Hypothesis
Null , There Is No-Significance between them Ho: u1 < u2
Alternate,mean number of words recaled after 1 hourv exceeds
the mean recall after 24 hours - H1: u1 > u2
Test Statistic
X(Mean)=13.6
Standard Deviation(s.d1)=2.7019 ; Number(n1)=5
Y(Mean)=12
Standard Deviation(s.d2)=2.1213; Number(n2)=5
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =13.6-12/Sqrt((7.30026/5)+(4.49991/5))
to =1.042
| to | =1.042
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 4 d.f is 1.533
We got |to| = 1.0415 & | t | = 1.533
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Right Tail -Ha : ( P > 1.0415 ) = 0.17823
Hence Value of P0.1 < 0.17823,Here We Do not Reject Ho

We have evidence that mean number of words recaled after 1 hourv exceeds
the mean recall after 24 hours

[ANSWERS
a. Ho: u1 < u2 , H1: u1 > u2
b. to =1.042
c. p = 0.17823
d. Yes, we have evidence

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