5 In the absence of special preparation SAT math scores in r

5. In the absence of special preparation, SAT math scores in recent years have varied normally with a mean of 518 and a standard deviation of 114. One hundred students go through a rigorous training program designed to raise their S average SAT math score after this training was 533.7. Is there significance at the 10% level that the mean SAT score after all the students go through a rigorous training is greater than 518? Use standard deviation of 114 as the population standard deviation. AT math scores. Their

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   518  
Ha:    u   >   518  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha =    0.1          
zcrit =    +   1.281551566      
              
Getting the test statistic, as              
              
X = sample mean =    533.7          
uo = hypothesized mean =    518          
n = sample size =    100          
s = standard deviation =    114          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.377192982          
              
Also, the p value is              
              
p =    0.084226295          
              
As z > 1.28, and P < 0.10, we   REJECT THE NULL HYPOTHESIS.          

There is significant evidence that the mean SAT score after all the students go through rigorous training is greater than 518. [CONCLUSION]

b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    533.7          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    114          
n = sample size =    100          
              
Thus,              
Margin of Error E =    29.36445406          
Lower bound =    504.3355459          
Upper bound =    563.0644541          
              
Thus, the confidence interval is              
              
(   504.3355459   ,   563.0644541   ) [ANSWER]