AP Statistics 3.2.C Sample Proportion Probabilities

Practise calculating probabilities for sample proportions by standardizing a cutoff with the population proportion and standard error, then selecting the correct tail.

Exam points

Standardize a sample-proportion cutoff with the reported population proportion and standard error.
Match at least or greater-than wording to the correct upper-tail normal probability.

[Maximum number: 1]

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 $H_0:p=0.403$ and $H_a:p>0.403$ .

Calculate the probability that the null hypothesis is rejected.

$P(\hat p>0.4837)=P\!\left(Z>(0.4837-0.45)/0.04975\right)=0.249$ .

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3.2.C—Interpret the mean, standard deviation, and probabilities for a sampling distribution of a sample proportion question 1