Solve the following problems. Show all solutions. Round off final answers to 3 d

Question

Solve the following problems. Show all solutions. Round off final answers to 3 decimal places.
1. The quality control manager at light bulb factory needs to determine whether the mean life of large shipment of light bulbs is equal to 370 hours. A random sample of 70 light bulbs with the mean life of 345 hours and standard deviation is 9.9 hours. Use the significance level of 0.025. Report with p- value.
A. Formulate the null and alternative hypothesis B. State the decision rule.
C. The test statistic
D. Conclusion

Explanation / Answer

1.

Given that,
population mean(u)=370
sample mean, x =345
standard deviation, s =9.9
number (n)=70
null, Ho: =370
alternate, H1: !=370
level of significance, = 0.025
from standard normal table, two tailed t /2 =2.291
since our test is two-tailed
reject Ho, if to < -2.291 OR if to > 2.291
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =345-370/(9.9/sqrt(70))
to =-21.128
| to | =21.128
critical value
the value of |t | with n-1 = 69 d.f is 2.291
we got |to| =21.128 & | t | =2.291
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -21.1278 ) = 0
hence value of p0.025 > 0,here we reject Ho
ANSWERS
---------------
A.
null, Ho: =370
alternate, H1: !=370
c.
test statistic: -21.128
critical value: -2.291 , 2.291
B.
decision: reject Ho
p-value: 0
D.
we have enough evidence to support the claim that mean life of large shipment of light bulbs is equal to 370 hours

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