In a study of the relationship between birth order and university success, an investigator found that 123 in a sample of 160 university graduates were firstborn or only children. In a sample of
100 non-graduates of comparable age and socioeconomic background, the number of firstborn or only children was 56. Estimate the difference between the proportions of firstborn or only children in the
two populations from which these samples were drawn ($p_1 - p_2$). Use a 90% confidence interval. (Use $p_1$ and $p_2$ for the proportions of firstborn or only children who were university graduates and non-
graduates, respectively. Round your answers to three decimal places.)
to
Interpret your results.
O In repeated sampling, 10% of all intervals constructed in this manner will enclose the true value of $p_1 - p_2$.
O In repeated sampling, 90% of all intervals constructed in this manner will enclose the true value of $p_1 - p_2$.
90% of all proportions will fall within the interval.
O There is a 10% chance that a single difference in sample proportions will fall within the interval.
O There is a 90% chance that a single difference in sample proportions will fall within the interval.
