Section 4.1: 13 ( use Excel; show the formula that was used to compute each valu
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Question
Section 4.1: 13 (use Excel; show the formula that was used to compute each value in the cell next to the value - you can do that by not having an equal sign in front of the formula),
13. A certain large shipment comes with a guarantee that it contains no more than 15% defective items. If the proportion of defective items in the shipment is greater than 15%, the shipment may be returned. You draw a random sample of 10 items. Let X be the number of defective items in the sample. a. If in fact 15% of the items in the shipment are defective (so that the shipment is good, but just barely), what is POX 7)? b. Based on the answer to part (a), if 15% ofthe items in the shipment are defective, would 7 defectives in a sample of size 10 be an unusually large number? c. If you found that 7 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain. d. If in fact 15% of the items in the shipment are defective, what is PCK 2 2? e. Based on the answer to part (d), if 15% of the items in the shipment are defective, would 2defectives in a sample of size 10 be an unusually large number? f. If you found that 2 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.Explanation / Answer
Result:
a).
P( x 7) = 1- P( x 6)
Excel function:
=1-BINOM.DIST(6,10,0.15,TRUE)
P( x 7) = 0.000135
b).
7 defects in sample of 10 is unusually large because P( x 7) is small ( < 0.05).
c).
yes, shipment should be returned.
d).
P( x 2) = 1- P( x 1)
Excel function:
=1-BINOM.DIST(1,10,0.15,TRUE)
P( x 2) = 0.4557
e).
2 defects in sample of 10 is not unusually large because P( x 2) is large (>0.05)
f).
No, there is no convincing evidence that shipment should be returned.
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