Confidence interval

A food testing laboratory in Abu Dhabi has been commissioned to estimate the amount of olive oil contained in 1-gallon tins purchased from a range of international olive oil producers. The manufacturers state that the standard deviation of the amount of olive oil is equal to 0.02 gallons. A random sample of 50 tins is selected, and the mean sample amount of olive oil per 1-gallon tin is 0.995 gallons.

A) Construct a 99% confidence interval estimate of the population mean amount of olive oil included in a 1-gallon tin.
B) based on these results, do you think the retailers have the right to complain to the manufacturers? Why or why not?
C) Construct a 95% confidence interval estimate. How does your answer under b) change?

Result

a =  0.9484
b =  1.0516
B=

Yes

No

Step-by-step explanation:

$$\begin{gathered} n=50 \\ m=1\text{gal} \\ \sigma =0.02\text{gal} \\ z=2.58 \\ a=m-z\cdot \sigma =1-2.58\cdot 0.02=0.9484 \end{gathered}$$

$b=m+z\cdot \sigma =1+2.58\cdot 0.02=1.0516$

$$\begin{gathered} 0.995\in <a;b> \\ B=1 \end{gathered}$$

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