1. A manufacturing firm wants to determine if there is a difference in the price
ID: 3324545 • Letter: 1
Question
1. A manufacturing firm wants to determine if there is a difference in the prices charged by two competing shipping companies State the null and alternative hypotheses. Company A Company B Using identical shipping requirements, they sample shipping costs for equal loads from both companies. Test at a 0.05 level of significance. Sample size Mean costs Sample standard deviation 57 $244.50 6 65 $239.7 7 Calculate the critical value (to 3 decimals). Calculate the test statistic (to 2 decimals). Using the Critical Value Approach, what decision should be made and WHY? What is the estimated p-value (to 3 decimals)? Using the pvalue Approach, what decision should be made and WHY?Explanation / Answer
Given that,
mean(x)=244.5
standard deviation , s.d1=6
number(n1)=57
y(mean)=239.7
standard deviation, s.d2 =7
number(n2)=65
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.003
since our test is two-tailed
reject Ho, if to < -2.003 OR if to > 2.003
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =244.5-239.7/sqrt((36/57)+(49/65))
to =4.078
| to | =4.078
critical value
the value of |t | with min (n1-1, n2-1) i.e 56 d.f is 2.003
we got |to| = 4.07802 & | t | = 2.003
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 4.078 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 4.078
critical value: -2.003 , 2.003
decision: reject Ho
p-value: 0
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