After the Moen has instituted a new manufacturing process for assembling a compo
ID: 3325223 • Letter: A
Question
After the Moen has instituted a new manufacturing process for assembling a component. Using the old process, the average assembly time was 4.25 minutes per component new process was in place for 30 days, the quality control engineer took a random sample of fourteen components and noted the time it took to assemble each component Based on the sample data, the average assembly time was 4.38 minutes, with a standard deviation of 16 minutes. Using a significance level of 02, has the new manutacturing process significantly changed the average assembly time? Do a complete and appropriate hypothesis test. Mo. Ha: 425 4.25 Using only the appropriate statistical table in your textbook, the critical value for rejecting Ho is 2282 (report your answer to 3 decimal places, using 304 (report your answer to 2 decimal places, using conventional rounding Using the sample data, the calculated value of the test statistic is rules) Should the null hypothesis be rejected? yes Has the new manufacturing process significantly changed the average assembly time? yes Using only the appropriate statistical table in your textbook, what is the most accurate statement you can make about the numerical value of the p-value of this hypothesis test? Answer The p-value ofre test statne is co47 which means (provide a one-sentence statement about the p-value)Explanation / Answer
Given that,
population mean(u)=4.25
sample mean, x =4.38
standard deviation, s =0.16
number (n)=14
null, Ho: =4.25
alternate, H1: !=4.25
level of significance, = 0.02
from standard normal table, two tailed t /2 =2.65
since our test is two-tailed
reject Ho, if to < -2.65 OR if to > 2.65
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =4.38-4.25/(0.16/sqrt(14))
to =3.04
| to | =3.04
critical value
the value of |t | with n-1 = 13 d.f is 2.65
we got |to| =3.04 & | t | =2.65
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 3.0401 ) = 0.0095
hence value of p0.02 > 0.0095,here we reject Ho
ANSWERS
---------------
null, Ho: =4.25
alternate, H1: !=4.25
test statistic: 3.04
critical value: -2.65 , 2.65
decision: reject Ho
p-value: 0.0095
we have enough evidence to support the claim that new manufacturing process for assembling a component