1260 (Problem 7) Taking an SAT preparatory course is believed to improve test sc

Question

1260

(Problem 7) Taking an SAT preparatory course is believed to improve test scores. To investigate the effects of taking a preparatory course, scores were recorded for 5 students before and and after they took the preparatory course. Does the data below suggest that a preparatory course increases test scores? Assume we want a 90% confidence level (=0.10) to test the claim. HINT: Assume the null hypothesis is that test scores stay the same, before and after taking the course. Also, assume the “expected” change in test scores is zero when evaluating the test statistic. (3 points each, 15 points total)

(a) Identify the alternate hypothesis
(b) What is the random variable (X) that we want to evaluate? (c) Find the test statistic (show all work)
(d) Find the P-value (show all work)
(e) Is there sufficient evidence to support the claim that taking a preparatory course increases an SAT test score? Justify your conclusion.

Student Before After 1 1200

1260

2 1150 1120 3 1260 1260 4 1050 1200 5 980 1050

Explanation / Answer

Consider the table:

Let

group 1 = before group
group 2 = after group

Let ud = u2 - u1.  
          
Formulating the null and alternative hypotheses,              
              
Ho:   ud   <=   0  
Ha:   ud   >   0   [ANSWER, A]

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b)

we want to evaluate the difference between the test scores before and after the course.

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c)

At level of significance =    0.1          

As we can see, this is a    right   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    49.25967064          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    22.02959442          
              
Calculating the mean of the differences (third column):              
              
XD =    50          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    2.269674105       [ANSWER, TEST STATISTIC]

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D)
              
As df = n - 1 =    4          
              
Thus, using p values,              
              
p =        0.042879254   [ANSWER, P VALUE]

****************************
              
Also, comparing this p to the significance level,   WE REJECT THE NULL HYPOTHESIS.          

Thus, there is sufficient evidence to support the claim that taking a preparatory course increases an SAT test score. [CONCLUSION]              

Before After Difference 1200 1260 60 1150 1120 -30 1260 1260 0 1050 1200 150 980 1050 70

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