Question 141844: 9.65 A consumer agency tested 290 hams, finding that 64 were underweight. (a) Construct a 95 percent
confidence interval for the true percent of underweight hams. (b) If the goal is to reduce the incidence
of underweight hams to 25 percent or less, does this sample show that the goal is being
achieved? (c) Explain how this confidence interval is equivalent to a two-tailed test at α = .05.
(Data are from Detroit Free Press, March 9, 1999, p. 2A.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A consumer agency tested 290 hams, finding that 64 were underweight.
(a) Construct a 95 percent confidence interval for the true percent of underweight hams.
p-hat = 64/290 = 0.22
E = 1.96sqrt(0.22*0.78/290) = 0.024
95% CI: 0.22-0.024 < p < 0.22+0.024
: 0.196 < p < 0.22024
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(b) If the goal is to reduce the incidence of under weight hams to 25 percent or less, does this sample show that the goal is being achieved?
No, we have 95% confidence that p is between 19.6% and 22%
That interval does not include 25%
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(c) Explain how this confidence interval is equivalent to a two-tailed test at α = .05.
I'll leave that to you.
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Cheers,
Stan H.
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