PROBLEM : Are the contributions statistically significant equal? Test at .01 sig

Question

PROBLEM :

Are the contributions statistically significant equal? Test at .01 significance level

Men: Average gross income = $48,500;   standard deviation = $1,000;   

n = 18 employees

Women: Average gross income = $43,600;   standard deviation = $2,000;   

n = 11 employees

PROBLEM :

Can we conclude that the toys of the two companies are equal when it comes to toy life.

Test at .05 significance level

ToysRUs: Average toy life= 14.50 years;   standard deviation = 1.50 years;    n = 10

TeddyBear store claimed: Average toy life = 13.60 years;   standard deviation = 2.10 years;    n = 11

Explanation / Answer

Given that,
mean(x)=48500
standard deviation , 1 =1000
number(n1)=18
y(mean)=43600
standard deviation, 2 =2000
number(n2)=11
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=48500-43600/sqrt((1000000/18)+(4000000/11))
zo =7.57
| zo | =7.57
critical value
the value of |z | at los 0.01% is 2.576
we got |zo | =7.568 & | z | =2.576
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 7.57 ) = 0
hence value of p0.01 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: 7.57
critical value: -2.576 , 2.576
decision: reject Ho
p-value: 0
contributions statistically significant are not equal

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

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