According to the U.S. Department of Agriculture, 58.8% of males between 20 and 3

Question

According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium. After an aggressive “Got milk” advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and found that 36 of them consume the recommended daily allowance of calcium.

a) Construct a 99% confidence interval for the above data. Show your work using the formulas and verify your work using StatCrunch.

b) Interpret the above confidence interval as we learned in class.

c) Construct a 90% confidence interval for the above data. Show your work using the formulas and verify your work using StatCrunch.

d) Explain why the widths of the two confidence intervals are different. Please explain each step clearly. Thank you

Explanation / Answer

alpha = 1 - 0.99 = 0.01

alpha / 2 = 0.005 Z = 2.57

p = 36 / 55 =0.65

0.65 +/- 2.57 * SRQT ( 0.65*0.35 / 55 )

0.65 +/- 0.165

0.485 < P < 0.815

B) WE ARE 99% CONFIDENT THAT THE TRUE PROPORTION OF males between 20 and 39 years old consume the minimum daily requirement of calcium IS BETWEEN INSIDE OF THE INTERVAL

c) alpha / 2 = 0.05 Z= 1.64

0.65 +/- 1.64 * SRQT ( 0.65*0.35 / 55 )

0.65 +/- 0.105

0.545 < p < 0.755

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