Problem 2: Got Milk (20 Points) According to the U.S. Department of Agriculture,

Question

Problem 2: Got Milk (20 Points) According to the U.S. Department of Agriculture, 52.8% 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) Calculate “by hand” (using the formulas discussed in class) a 99% confidence interval for the proportion of males between the ages of 20 and 39 that consume the minimum daily requirement of calcium after the “Got Milk“ campaign. Show your work. Specifically, show the calculation of the sample proportion, the estimated standard error, the margin of error, and the limits of the confidence interval.

b) Verify your answer to Part a using StatCrunch. For this part (Part b), just include a copy of the table from the StatCrunch output showing the confidence interval.

c) Interpret this 99% confidence interval in context of the data (as we discussed in class).

d) Based on this 99% confidence interval, should the USDA consider their campaign successful? Explain.

e) Repeat Part a using a 90% confidence level.

f) Verify your answer to Part e using StatCrunch. For this part (Part f), just include a copy of the table from the StatCrunch output showing the confidence interval. g) Based on this 90% confidence interval, should the USDA consider their campaign successful? Explain.

h) Are your answers to Parts d and g contradictory? Why or why not?

Explanation / Answer

a) The 99% c.i=Ps+-Z sqrt [Pu(1-Pu)/N], where, Ps and Pu are sample and population proportion, N is sample size, Z correspinds to z score at alpha=0.01

=36/55+-2.58 sqrt[0.528(1-0.528)/55]

=0.4808 to 0.8282

c) One can be 99% confident that the true population of men aged 20-39 consume the recommended daily allowance of calcium is between 0.4808 to 0.8282.

d) The confidence interval show sthat more than 50% of men aged 20-39 consume the recommended daily allownace of calcium, therefore, USDA consider their campaign successful.

e) 90% c.i= Ps+-Z sqrt [Pu(1-Pu)/N]

=36/55+-1.65 sqrt[0.528(1-0.528)/55]

=0.6471 to 0.7656

g) With decrease in confidence level, the interval width decrased, but still more than 50% of men of age 20-39 are supposed to consume recommended daily allowance of calcium. The campaign is successful.

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