In recent years, the US and Japan have engaged in intense negotiations regarding
ID: 3223259 • Letter: I
Question
In recent years, the US and Japan have engaged in intense negotiations regarding restrictions on trade between the two countries. An economist decides to test the hypothesis that higher retail prices are being charged for Japanese automobiles in Japan than in US., She randomly obtained a sample retail sales in the US and 30 retail sales in Japan over the same time period and for the same automobile. A summary table is below: A manufacturing operation consists of a single-machine-tool system that produces an average of 15.5 transformer parts every hour. The production of transformers is assumed to be normally distributed. The system was monitored and observed the number of parts produced in each of 17 randomly selected one-hour periods. The mean and standard deviation of the 17 production nuns are 15.42 and 0.16, respectively. Does this provide evidence that the true mean number of parts produced every hour differs from 15.5? Test at alpha = 0.05 According to a CCH Unscheduled Absence Survey, 9% of small businesses use telecommunicating of workers in an effort to reduce unscheduled absenteeism. This proportion compares to 6% for all businesses. Is there really a significant difference between small business and all business in this issue? Use the data and an alpha of 0.1 to test this question. Assume there were 780 small businesses and 915 other businesses in this survey.Explanation / Answer
4.
Given that,
mean(x)=17243
standard deviation , s.d1=1843
number(n1)=30
y(mean)=16545
standard deviation, s.d2 =1989
number(n2)=50
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.699
since our test is right-tailed
reject Ho, if to > 1.699
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =17243-16545/sqrt((3396649/30)+(3956121/50))
to =1.592
| to | =1.592
critical value
the value of |t | with min (n1-1, n2-1) i.e 29 d.f is 1.699
we got |to| = 1.59153 & | t | = 1.699
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 1.5915 ) = 0.06117
hence value of p0.05 < 0.06117,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 1.592
critical value: 1.699
decision: do not reject Ho
p-value: 0.06117
we don't have evidence to support higher retail prices are being charged for japanese automobiles when compared to US
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