5. In the absence of special preparation, SAT math scores in recent years have v
ID: 3396161 • Letter: 5
Question
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. TheirExplanation / Answer
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]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.