Pennies mintes after 1982 are made from 97.5% zinc and 2.5% copper. The followin

Question

Pennies mintes after 1982 are made from 97.5% zinc and 2.5% copper. The following data represent the weights (in grams) of 17 randomly selected pennies minted after 1982.

2.46 2.47 2.49 2.48 2.50 2.44 2.46 2.45

2.49 2.47 2.45 2.46 2.45 2.46 2.47 2.44 2.45

a) What does the confidence interval suggest about a penny that weighs 2.51 grams. What might you conclude?

b) What sample size of pennies minted after 1982 should be obtained if we wish to estimate the percentage to be within 3 percentage points with 90% confidence? Assume Standard Deviation = 0.02 grams.

Explanation / Answer

SolutionA:

x bar=sum/tot=41.89/17=2.464

standard deviation=s=0.017698

n=sample size=17

95% confidence interval for true mean is

xbar-tcrit*s/sqrt(n),xbar+tcrit*s/sqrt(n)

2.464-2.12*0.17698/sqrt(17),2.464+2.12*0.17698/sqrt(17),

2.455,2.473

lower limit=2.455

upper limit=2.473

the confidence interval suggest that a penny that weighs 2.51 grams. is outside the limits .

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