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

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. Use z-table.

Show the sampling distribution of ( ), the proportion of groceries thrown out by your sample respondents (to 4 decimals).

SelectCannot assumed to be normally distributedCan assume to be normally distributed because n>=30 and sigma is givenCan assume to be normally distributed because n>100Can assume to be normally distributed because the underlying population is normally distributed and sigma is givenCan assume to be normally distributed because np>=5 and n(1-p)>=5Item 1

p =

standard error of the proportion () =

What is the probability that your survey will provide a sample proportion within ±.03 of the population proportion (to 4 decimals)?

What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion (to 4 decimals)?

Explanation / Answer

Can assume to be normally distributed because np>=5 and n(1-p)>=5

p=0.12

standard error of the proportion (p)=(p(1-p)/n)1/2 =0.0140

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

=P(-0.03/0.0140<Z<0.03/0.0140)=P(-2.1453<Z<2.1453)=0.9840-0.0159=0.9681

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

=P(-0.15/0.0140<Z<0.15/0.0140)=P(-10.7265<Z<10.7265)=~1 - ~0 =1.0000

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.