A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90 percent confidence interval for the true mean weight of bags of grapes from this store to be open paren 15 point 8 7 5 comma 16 point 5 9 5 close paren ounces. What is the sample mean weight of grapes, and what is the margin of error?
Answer
A
The sample mean weight is 15 point 8 7 5 ounces, and the margin of error is 16 point 5 9 5 ounces.
B
The sample mean weight is 16 point 2 3 5 ounces, and the margin of error is 0 point 3 6 0 ounces.
C
The sample mean weight is 16 ounces, and the margin of error is 0 point 7 2 0 ounces.
D
The sample mean weight is 16 point 2 3 5 ounces, and the margin of error is 0 point 7 2 0 ounces.
Explanation
The sample mean is the midpoint of the confidence interval: (15.875 + 16.595) ÷ 2 = 16.235 ounces. The margin of error is half the interval’s width: (16.595 − 15.875) ÷ 2 = 0.360 ounces. So the sample mean is 16.235 ounces and the margin of error is 0.360 ounces.
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