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Math·Problem-Solving and Data Analysis·Inference from sample statistics and margin of error

hard

A snack company advertises that bags of pretzels produced by the company weigh, on average, $1\text{ pound}$ each. To test this, Sam selected at random $40$ bags of pretzels produced by the company and weighed each bag. Based on his measurements, Sam estimated that for all bags of pretzels produced by the company, the average weight per bag is $1.05\text{ pounds}$, with a margin of error of $0.06\text{ pounds}$. For all bags of pretzels produced by the company, which of the following is the most appropriate conclusion about the average weight $w$, in pounds, per bag?

A

$0.99\le w\le 1.05$

B

$w=1.05$

C

$1.05\le w\le 1.11$

D

$0.99\le w\le 1.11$