Answer:
Consider the following calculations
Explanation:
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.
a- Show the sampling distribution of ( p¯ ), the proportion of groceries thrown out by your sample respondents
sampling distribution of ( p¯ ) is normal with
mean = 0.12 and
standard error = sqrt(p(1-p)/n) = sqrt(0.12*0.88/540) =0.0140
b- what is the probability that the sample proportion will be within ±.03 of the population proportion?
z value for 0.03 difference, z=0.03/0.014 =2.14
The required P= P( -2.14<z<2.14) = P( z <2.14) – P( z <-2.14)
=0.9838 - 0.0162
=0.9676
c- what is the probability that your survey will provide a sample proportion within ±.015 of the population proportion?
z value for 0.015 difference, z=0.015/0.014 =1.07
The required P= P( -1.07<z<1.07) = P( z <1.07) – P( z <-1.07)
=0.8577 - 0.1423
=0.7154
d- What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why?
Taking a larger sample will decrease the standard error. The probabilities in parts (b) and (c) will increase.
