Question

2)A study was conducted by a local city council to determine if the salaries of librarians from two neighboring cities were equal. A sampleof15librariansfromeachcitywasrandomlyselected.Themeanfromthefirstcitywas$28,900witha standarddeviationof$2300.Themeanfromthesecondcitywas$30,300withastandarddeviationof$2100. Analysis the data using a hypothesis test and advise the council of your findings.Use=0.05

.a)Hypothesis:

b)Critical value (tcritical):

c)Test statistic(tstat)and the decision about the test statistic:(reject or fail to reject Ho):

d)Conclusion that results from the decision about Ho:

Answer 1

2. Given that,
mean(x)=28900
standard deviation , s.d1=2300
number(n1)=15
y(mean)=30300
standard deviation, s.d2 =2100
number(n2)=15
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.145
since our test is two-tailed
reject Ho, if to < -2.145 OR if to > 2.145
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =28900-30300/sqrt((5290000/15)+(4410000/15))
to =-1.741
| to | =1.741
critical value
the value of |t α| with min (n1-1, n2-1) i.e 14 d.f is 2.145
we got |to| = 1.74096 & | t α | = 2.145
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.741 ) = 0.104
hence value of p0.05 < 0.104,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: u1 = u2
alternate, H1: u1 != u2
c.
test statistic: -1.741
b.
critical value: -2.145 , 2.145
decision: do not reject Ho
p-value: 0.104
d.
we do not have enough evidence to support the claim that if the salaries of librarians from two neighboring cities were equal.