Paired data arise from studies in which one is testing to see whether a new trea
ID: 3209573 • Letter: P
Question
Paired data arise from studies in which one is testing to see whether a new treatment technique, or method works better than an existing method, without having to worry about other variables and their effects. Often the samples are paired up in some way or the same people are used twice (e.g. pre-test and post-test). As an example, reading accuracy was compared by using printed (paper) email messages versus reading directly from the mobile device. Reading (comprehension) scores for 10 individuals are reported below. State Ho and Ha Apply the appropriate 2-sample t test statistic Specify a 95% confidence interval for the mean improvement of the entire population. What did you choose/calculate as the value for the degrees of freedom? Could another choice be valid or justified?Explanation / Answer
(1) Ho: 1 = 2 (or d-bar = 0) versus Ha: 1 2 (or d-bar 0)
(2)
Data:
n = n1 = n2 = 10
d-bar = 2
s (of d) = 4.642796092
Hypotheses:
Ho: 1 = 2
Ha: 1 2
Decision Rule:
= 0.05
Degrees of freedom = 10 - 1 = 9
Lower Critical t- score = -2.262157158
Upper Critical t- score = 2.262157158
Reject Ho if |t| > 2.262157158
Test Statistic:
SE = s/n = 4.64279609239471/10 = 1.468181036
t = d-bar/SE = 2/1.46818103636968 = 1.362229828
(3)
n1 = n2 = n = 10
d-bar = 2
s of d-bar = 4.6428
% = 95
Degrees of freedom = n - 1 = 9
SE = s/n = 1.468182272
t- score = 2.262157158
Width of the confidence interval = t * SE = 3.321259036
Lower limit of the confidence interval = d-bar - width = -1.321259036
Upper limit of the confidence interval = d-bar + width = 5.321259036
The 95% confidence interval is [-1.321 , 5.321]
(4) Degrees of freedom = 10 - 1 = 9
(5) No other value for degrees of freedom can be assumed since this is a paired test.
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