The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.
Given the true proportion is 0.07, sample size 289.
We have to calculate the probability that the sample proportion will differ from the population proportion by more than 0.03.
Probability is the likeliness or chance of happening an event among all the events possible. The probability lies between 0 and 1.
Probability=number of items/ total items.
True proportion=0.07
n=289
sample population mean=0.07
Sample proportion standard error=[tex]\sqrt{pq/n}[/tex]
=[tex]\sqrt{0.07*0.93)/289}[/tex]
=[tex]\sqrt{0.0651/289}[/tex]
=[tex]\sqrt{0.00022}[/tex]
=0.015
Probability that the sample proportion will differ from the population proportion by more than 0.03=P(I P-p I>0.03)
=P( I Z I>0.03*0.015)
=P ( I z I >0.0045)
=0.99968.
Hence the probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.
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