Confidence intervals with Z,X2 and t random variables Suppose that a machine fil

Question

Confidence intervals with Z,X2 and t random variables Suppose that a machine fills can is 30.0 fluid ounces. Let four cans, obtaining the sample empty cans with paint, The machine is calibrated correctly if the average amount of paint per be the average amount of paint per can. Suppose that we measure the amounts of paint in 29.0, 30.5, 30.1, 28.5 where the valucs are amounts of paint in fuid ounces I. Assuming a known vul ue of 90% confidence interval for . 1.0 ounces for the standard deviation of the amount of paint in one ean, calculate a 2. Assuming that is unknown but the amounts of paint in each can are approc mately norma calculate a confidence interval for , Find a 90% confidence interval for the standard deviation of the amount of paint the machine puts in a can. 4. Repeat the above exercises using a 99% confidence level instead.

Explanation / Answer

Solution1:

sd=1

use z distribution

Z crit=1.645

90% confidence interval for mean is

sample mean-z cri(pop sd/sqrt(n),sample mean+z cri(pop sd/sqrt(n)

sample mean=sum/total=29+30.5+30.1+28.5/4

=29.525

therofre

29.525-1.645(1/sqrt(4),29.525+1.645(1/sqrt(4)

28.7025,30.3475

lower limit=28.7025

upper limit=30.3475

we are 90% confident that the true population mean lies in between

28.7025 and 30.3475

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---