The standard error (SE) of a statistic is the approximate standard deviation of a statistical sample population. The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, a sample mean deviates from the actual mean of a population—this deviation is the standard error of the mean.The sample proportion is a random variable: it varies from sample to sample in a way that cannot be predicted with certainty.

For, Sample proportion, p,σ_p=sqrt [ P(1 - P) / n ]

in this case,

Proportion of successes in population, P=.23

Number of observations in the sample,n=240

  sample deviation, σ_p=sqrt [ P(1 - P) / n ]

=sqrt[.23(1-.23)/240]

=sqrt[1.771/240]

=sqrt[.000738]

=.0272

B) Z= ( pˆ- μPˆ)/ σ_{p =}  (pˆ-P ) / (sqrt [ P(1 - P) / n ])

P = 43/240=0.1792

the probability that the sample proportion is no more than that found in the survey

i.e Pr<=P.

Pr(P<=.1792)= Pr(Z<=(.1792-.23)/0.0272)

=Pr(z<=-1.87)

From the probability table given below,we can find the value of Pr(z<=-1.87)

i.e the probability that the sample proportion is no more than that found in the survey

equals to .0307 please see the attached file.