A manefacturer of banasa chigs would lae so Lnow whether its bag filling nachine

Question

A manefacturer of banasa chigs would lae so Lnow whether its bag filling nachine works soectly at the 416 gram seing bags. A 3Sbag sample hala mean of 412 grams at the O.1 level of sigsificance that the bags are underfitled Le-Tailed T A Sumber company is mking dooes that are 2038.0 millenetors all. ir as dors anve too long they must be trimmed. and ir la detrs with a standard devistion of 21.0. A level ef significance of 0 I will be used to determine if the doors arc cither 1oo kong or too short. Find the rvalue of the lest statistic. Round your answer to 3 decimal places. Assume the population 20. (3 Poinks) 11. A manufacturer of chocolae chips would like to know whether is bag filling machine works correctly at the 445 gram setting. It is believed that the machine is underfilling the bags. A 27 bag sample had deviation of 19. A level of significance of 0.025 will be used. Determine the decisice rule. Assume the distribution is approximately normal. a mean of 442 grams with a standard (3 Points) Reject Hy ift

Explanation / Answer

QUESTION 11.
Given that,
population mean(u)=445
sample mean, x =442
standard deviation, s =19
number (n)=27
null, Ho: =445
alternate, H1: !=445
level of significance, = 0.025
from standard normal table, two tailed t /2 =2.379
since our test is two-tailed
reject Ho, if to < -2.379 OR if to > 2.379
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =442-445/(19/sqrt(27))
to =-0.8204
| to | =0.8204
critical value
the value of |t | with n-1 = 26 d.f is 2.379
we got |to| =0.8204 & | t | =2.379
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -0.8204 ) = 0.4194
hence value of p0.025 < 0.4194,here we do not reject Ho
ANSWERS
---------------
null, Ho: =445
alternate, H1: !=445
test statistic: -0.8204
critical value: -2.379 , 2.379
decision: do not reject Ho
p-value: 0.4194

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