People end up tossing 12% of what they buy at the grocery store (Reader’s Digest

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. Show the sampling distribution of p, the proportion of groceries thrown out by your sample respondents. What is the probability that your survey will provide a sample proportion within 6.03 of the population proportion? What is the probability that your survey will provide a sample proportion within 6.015 of the population proportion? 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. Show the sampling distribution of p, the proportion of groceries thrown out by your sample respondents. What is the probability that your survey will provide a sample proportion within 6.03 of the population proportion? What is the probability that your survey will provide a sample proportion within 6.015 of the population proportion?

Explanation / Answer

a] the sampling distribution of p,

ie, p=0.12

the proportion of groceries, s=sqrt[0.12*0.88/540]

s=0.01

b] probability that survey will provide sample proportion with 6.03 is

0.12+6.03=6.15

now,

z(6.15)=(6.15-0.12)/sqrt(0.12*0.88/540)

= 0.0603

c] similarly probability provide sample proportion within 6.015 is

0.12+6.015=6.135

z(6.135)=(6.135-0.12)/sqrt(0.12*0.88/540)

=0.06015.

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