Question

According to a recent U.S. Bureau of Labor Statistics report, the proportion of married couples with children in which both parents work outside the home is 59%. You select an SRS of 50 married couples with children and let p = the sample proportion of couples in which both parents work outside the home.

a) Calculate the mean and the standard deviation of the sampling distribution of p^.

b) Would it be appropriate to use a normal distribution to model the sampling distribution of p^= the sample proportion of couples in which both parents work outside the home? Justify your answer.

Answer 1

P( married couples with children in which both parents work outside the home ) = 0.59 =   

Sample, n= 50

a) Mean of the sampling distribution of = 0.59

Sampling Deviation of = =    = 0.0695

b) Yes , it would be appropriate to use a normal distribution to model the sampling distribution of as the sample of the married couple we are using is n= 50 which is large enough (n>30) , so by Central limit Theorem we can use normal distribution to model the sampling distribution of .