A math teacher claims that she has developed a review course that increases the

Question

A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with mu equals 525. The teacher obtains a random sample of 2000 students, puts them through the review class, and finds that the mean math score of the 2000 students is 531 with a standard deviation of 113. Find the Test statistic. Find the P value.Is the sample mean statistically significantly higher? Do you think that a mean math score of 531 versus 525 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?

Explanation / Answer

Given that,
population mean(u)=525
sample mean, x =531
standard deviation, s =113
number (n)=2000
null, Ho: <525
alternate, H1: >525
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.646
since our test is right-tailed
reject Ho, if to > 1.646
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =531-525/(113/sqrt(2000))
to =2.375
| to | =2.375
critical value
the value of |t | with n-1 = 1999 d.f is 1.646
we got |to| =2.375 & | t | =1.646
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.3746 ) = 0.00883
hence value of p0.05 > 0.00883,here we reject Ho
ANSWERS
---------------
null, Ho: =525
alternate, H1: >525
test statistic: 2.375
critical value: 1.646
decision: reject Ho
p-value: 0.00883
sample mean statistically significantly higher

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