Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.
Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.
Five students took a math test before and after tutoring. Their scores were as follows.
Student 
A 
B 
C 
D 
E 
Before 
71 
66 
67 
77 
75 
After 
75 
75 
65 
80 
87 
Using a 0.01 level of significance, test the claim that the tutoring has a positive effect on the math scores.
1. State the null and alternative hypotheses.
Solution:

2. Find d, , and s_{d,. }Note: It doesn’t make any difference which row you subtract
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3. Find the value of the test statistic, t.
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4. Only Find the critical value(s) and state the decision about the null hypothesis using the test statistic and the critical value
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5. State the conclusion
in nontechnical terms.
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