A university is interested in promoting graduates of its honors program by estab

Question

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40.

Refer to Exhibit 9-1. At a 5% significance level, the decision is to _____________.

reject we can conclude that the mean GPA is significantly greater than 3.50

reject we cannot conclude that the mean GPA is significantly greater than 3.50

do not reject we can conclude that the mean GPA is significantly greater than 3.50

do not reject we cannot conclude that the mean GPA is significantly greater than 3.50

Explanation / Answer

Given that,
population mean(u)=3.5
standard deviation, =0.4
sample mean, x =3.6
number (n)=36
null, Ho: =3.5
alternate, H1: >3.5
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 3.6-3.5/(0.4/sqrt(36)
zo = 1.5
| zo | = 1.5
critical value
the value of |z | at los 5% is 1.645
we got |zo| =1.5 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : right tail - ha : ( p > 1.5 ) = 0.06681
hence value of p0.05 < 0.06681, here we do not reject Ho
ANSWERS
---------------
null, Ho: =3.5
alternate, H1: >3.5
test statistic: 1.5
critical value: 1.645
decision: do not reject Ho
p-value: 0.06681

do not reject Picture we cannot conclude that the mean GPA is significantly greater than 3.50

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