Please solve the following labeling each step of the hypothesis test (1: state t
ID: 3216697 • Letter: P
Question
Please solve the following labeling each step of the hypothesis test (1: state the null and alternative hypotheses; 2: state the significance level; 3: find the test statistic; 4: find the p-value; 5: make a decision; 6: state your conclusion)
The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Total scores on the GMAT are normally distributed. The Graduate Management Admission Council, who administers the test, claims that the mean total score is 529. Suppose a random sample of 8 students took the test, and their scores are given below.
699, 560, 414, 570, 521, 663, 727, 413
Use = .05 to test the claim that the mean total score is different from 529.
Explanation / Answer
Given that,
population mean(u)=529
sample mean, x =570.875
standard deviation, s =120.3678
number (n)=8
null, Ho: =529
alternate, H1: !=529
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.365
since our test is two-tailed
reject Ho, if to < -2.365 OR if to > 2.365
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =570.875-529/(120.3678/sqrt(8))
to =0.984
| to | =0.984
critical value
the value of |t | with n-1 = 7 d.f is 2.365
we got |to| =0.984 & | t | =2.365
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 0.984 ) = 0.3579
hence value of p0.05 < 0.3579,here we do not reject Ho
ANSWERS
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null, Ho: =529
alternate, H1: !=529
test statistic: 0.984
critical value: -2.365 , 2.365
decision: do not reject Ho
p-value: 0.3579