Question

The company estimated the mean of painting pages as 30000, the standard deviations as 1500 pages....

The company estimated the mean of painting pages as 30000, the standard deviations as 1500 pages. To test if the manager decision makes sense we have to conduct a statistical test to see if it is right or not. For the equation Ho: n= 285 or n>28500 Ha: n<28500, x = 0.05. The sample size will be 100, z= x- - μ/ σ/n = 30000 - 28500/ 1500/ 100 = 10. The sample size is any number between 4 or more, we get the get the calculated value of z will be greater then 2. Z critical value = -1.96, hence we accept Ho and conclude that the mean number of pages is greater then or equal to 28500. There fore the managers decision does make sense. He can keep the guaranteed number of pages more. In this case in the above calculation, we get the value of z slightly greater than -1.96 and we accept Ho at 5% level of significance. But if he guarantees more than 30295 he will loose money on product 95% of the time. I would be follow the managers business plan and keep the same equation, its safe and its productive.

Would you tell us why you need to conduct a statistical test? Is this issue about statistical test? Would you tell us how you would know that the sample size is 100? How would you know if the manager guarantees more than 30295 pages, then the company will loose money on product 95% of the time? Do you have any evidence and information to show us? Would you explain it to us in detail?

Math   Statistics-And-Probability   
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Answer #1

Given that,
population mean(u)=28500
standard deviation, σ =1500
sample mean, x =30000
number (n)=100
null, Ho: μ=28500
alternate, H1: μ>28500
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 30000-28500/(1500/sqrt(100)
zo = 10
| zo | = 10
critical value
the value of |z α| at los 5% is 1.645
we got |zo| =10 & | z α | = 1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : right tail - ha : ( p > 10 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: μ=28500
alternate, H1: μ>28500
test statistic: 10
critical value: 1.645
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that the mean number of pages is greater then or equal to 28500

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