Two packaging machines are to be tested to see if they are dispensing the same a
ID: 3179784 • Letter: T
Question
Two packaging machines are to be tested to see if they are dispensing the same amount. The variance (2) of the amount dispensed is 0.25 pounds for each machine. Ten packages are collected from each machine and weighed. The mean weight from the first machine is 8.77 pounds and the mean weight from the second machine is 9.12 pounds.
a) Perform a hypothesis test to determine whether there is evidence that the two machines are not dispensing the same mean amount. Assume a value of 0.05 for .
For your hypothesis tests, show your work for all 7 steps of the hypothesis test and label the steps (1, 2, ...). For step 7, state your conclusion using all 3 items specified for problem 4.
b) Determine the p-value for this test.
c) Based on your p-value from part (b), are you very confident or slightly confident in your
conclusion from part (a). Explain your reason.
d) Determine the test’s power to determine there has been a shift when the difference in
mean weights is 0.5 pounds.
Explanation / Answer
Given that,
mean(x)=8.77
standard deviation , 1 =0.5
number(n1)=10
y(mean)=9.12
standard deviation, 2 =0.5
number(n2)=10
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=8.77-9.12/sqrt((0.25/10)+(0.25/10))
zo =-1.57
| zo | =1.57
critical value
the value of |z | at los 0.05% is 1.96
we got |zo | =1.565 & | z | =1.96
make decision
hence value of | zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.57 ) = 0.11752
hence value of p0.05 < 0.11752,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: -1.57
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.11752
he two machines are not dispensing the same mean amount
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