Please help me figure this out as clear as you possible can because I can not un

Question

Please help me figure this out as clear as you possible can because I can not understand how everybody gets the answer Please help me figure this out as clear as you possible can because I can not understand how everybody gets the answer 7) 7) A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100, Test the hypothesis that the salaries from both cities are equal.

Explanation / Answer

Given that,
mean(x)=28900
standard deviation , s.d1=23000
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, = 0.05
from standard normal table, two tailed t /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((529000000/15)+(4410000/15))
to =-0.2348
| to | =0.2348
critical value
the value of |t | with min (n1-1, n2-1) i.e 14 d.f is 2.145
we got |to| = 0.23477 & | t | = 2.145
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.2348 ) = 0.818
hence value of p0.05 < 0.818,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -0.2348
critical value: -2.145 , 2.145
decision: do not reject Ho
p-value: 0.818

we have evidence that both means are equal

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.