The management of White Industries is considering a new method of assembling its
ID: 3223262 • Letter: T
Question
The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster? a. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) b. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) c. What is your decision regarding H_0? Fail to reject RejectExplanation / Answer
Given that,
population mean(u)=42.3
sample mean, x =40.6
standard deviation, s =2.7
number (n)=24
null, Ho: >42.3
alternate, H1: <42.3
level of significance, = 0.1
from standard normal table,left tailed t /2 =1.319
since our test is left-tailed
reject Ho, if to < -1.319
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =40.6-42.3/(2.7/sqrt(24))
to =-3.085
| to | =3.085
critical value
the value of |t | with n-1 = 23 d.f is 1.319
we got |to| =3.085 & | t | =1.319
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -3.0845 ) = 0.00262
hence value of p0.1 > 0.00262,here we reject Ho
ANSWERS
---------------
null, Ho: =42.3
alternate, H1: <42.3
test statistic: -3.085
critical value: -1.319
decision: reject Ho
p-value: 0.00262
a.
reject Ho, if to < -1.319
b.
test statistic: -3.085
c.
reject Ho, we support that assembly time using the new method is faster
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