Practise interpreting sample-proportion probabilities by standardising a contextual cutoff with the population proportion and standard error, then selecting its tail.
It was recently reported that in the United States, 40.3\% of all births are to unmarried mothers. A county health administrator is investigating whether births to unmarried women is higher in her county than in the national average. If so, she will propose additional funding to counsel unmarried mothers. A random sample of 100 births in the county will be looked at. Let p= the proportion of the population of women giving birth in the county who are unmarried. Consider the following hypotheses. The hypotheses are H0:p=0.403 and Ha:p>0.403.
Calculate the probability that the null hypothesis is rejected.
P(p^>0.4837)=P(Z>(0.4837−0.45)/0.04975)=0.249.