A machine that is programmed to package 1.20 pounds of cereal is being tested fo

Question

A machine that is programmed to package 1.20 pounds of cereal is being tested for accuracy. In a sample of 40 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. A) Identify the relevant perameter of interest for these quantitative data and compute its point estimate as well as the margin of error with 90% confidence. B) Can we conclude that the packaging machine is operating improperly? Prove your answer by estimating the 90% confidence interval for the mean. C) How large a sample must we take if we want the margin of error to be at most 0.01 pound with 90% confidence?

Explanation / Answer

a)

point estimate = sample mean = 1.22

since n = 40 > 30, we can estimate by z-test

margin of error = z * sd/sqrt(n)

=1.645*0.06/sqrt(40)=0.01560584025

b)

90% confidence interval = (point estimate +- margin of error)

= ( 1.22-0.01560584025 ,1.22+0.01560584025)

= (1.20439415975 , 1.23560584025)

since 1.2 is not present in confidence interval

we reject the null hypothesis and we conclude that the packaging machine is operating improperly

c)

n = z^2 * sd^2/e^2

= (1.645 * 0.06/0.01)^2

= 97.4169

n = 98

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