A machine that is programmed to package 4.85 pounds of cereal is being tested fo

Question

A machine that is programmed to package 4.85 pounds of cereal is being tested for its accuracy. In a sample of 81 cereal boxes, the sample mean filling weight is calculated as 4.85 pounds. It can be assumed that filling weights are normally distributed with a population standard deviation of 0.07 pound. Use Table 1.

Identify the relevant parameter of interest for these quantitative data.

Compute the point estimate as well as the margin of error with 95% confidence. (Round intermediate calculations to 4 decimal places. Round "z" value and final answers to 2 decimal places.)

Calculate the 95% confidence interval. (Use rounded margin of error. Round your answers to 2 decimal places.)

Can we conclude that the packaging machine is operating improperly?

How large a sample must we take if we want the margin of error to be at most 0.01 pound with 95% confidence? (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and round up your final answer to the next whole number.)

A machine that is programmed to package 4.85 pounds of cereal is being tested for its accuracy. In a sample of 81 cereal boxes, the sample mean filling weight is calculated as 4.85 pounds. It can be assumed that filling weights are normally distributed with a population standard deviation of 0.07 pound. Use Table 1.

Explanation / Answer

a.1. The parameter of interest is the average filling weight of all cereal packages

a.2. As sample is n=81, as per central limit theorem mean would be normally distributed with mu=4.85 and sd=sd/sqrt(n)=0.07/9=0.0078

Now as it is normally distributed and n>30 we will use z distribution, z value for 95% CI is 1.96

Hence Margin of Error=z#sd/sqrt(n)=1.96*0.0078=0.0153

b. 1. CI=mean+/-Margin of error=4.85+/-0.0153=(4.8347,4.8653)

b. 2. No, since the confidence interval contains the target filling weight of 4.85

c. Here E=0.01 and z=1.96 with sd=0.0078

Now using E formula we can find n

E=z*sd/sqrt(n)

So n=(z*sd/E)^2=2.33=2

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