In a study of memory recall, 5 people were given 10 minutes to memorize a list o

Question

In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table. 6. Number of Words Recalled Subject 1 hour later 24 hours later 13 18 10 15 12 16 13 Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Assume we want to use a 0.05 significance level to test the claim Identify the null hypothesis and the alternative hypothesis. work, will receive no credit. will recetve no credit hour exceeds the mean recall after 24 hours? Justify your conclusion. (a) (b) Determine the test statistic. Show all work, writing the correct test statistic, without supporting (c) Determine the P-value. Show all work writing the correct P-value, without supporting work (d) Is there sufficient evidence to support the claim that the mean number of words recalled after 1

Explanation / Answer

Given that,
null, H0: Ud < 0
alternate, H1: Ud > 0
level of significance, = 0.05
from standard normal table,right tailed t /2 =2.132
since our test is right-tailed
reject Ho, if to > 2.132
we use Test Statistic
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 1.2
We have d = 1.2
pooled variance = calculate value of Sd= S^2 = sqrt [ 10-(6^2/5 ] / 4 = 0.84
to = d/ (S/n) = 3.21
critical Value
the value of |t | with n-1 = 4 d.f is 2.132
we got |t o| = 3.21 & |t | =2.132
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 3.2071 ) = 0.01634
hence value of p0.05 > 0.01634,here we do not reject Ho
ANSWERS
---------------
null, H0: Ud < 0
alternate, H1: Ud > 0
test statistic: 3.21
critical value: reject Ho, if to > 2.132
decision: Reject Ho
p-value: 0.01634

we have evidence that no.of words recalled after 1 hour exceed the mean recall after 24 hours

1 Hour later 24 Hour later X-Y (X-Y)^2 13 12 1 1 18 16 2 4 10 9 1 1 15 13 2 4 6 10

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