People end up tossing 12% of what they buy at the grocery store (Reader\'s Diges

Question

People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March, 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior.

Round your answers to four decimal places.

a. Show the sampling distribution of p, the proportion of groceries thrown out by your sample respondents.

The distribution is

Mean =

=

b. What is the probability that your survey will provide a sample proportion within ±.03 of the population proportion?

c. What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion? In determining your answer, use the standard error found in part a. and the probability found using the tables in the text.

Explanation / Answer

a)

Mean =0.12

and std error =(p(1-p)/n)1/2 =0.0140

b)

probability that your survey will provide a sample proportion within ±.03 =P(-0.03/0.0140<Z<0.03/0.0140)

=P(-2.1453<Z<2.1453)=0.9840-0.0159 =0.9681

c)  probability that your survey will provide a sample proportion within ±.015 of the population proportion

=P(-0.015/0.0140<Z<0.015/0.0140)=P(-1.0726<Z<1.0726)=0.8583-0.1417 =0.7166

please revert for any clarification required

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