In a study of the relationship between birth order and university success, an in

Question

In a study of the relationship between birth order and university success, an investigator found that 123 in a sample of 150 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 59. Estimate the difference between the proportions of firstborn or only children in the two populations from which these samples were drawn (p1 p2). Use a 90% confidence interval. (Use p1 and p2 for the proportions of firstborn or only children who were university graduates and non-graduates, respectively. Round your answers to three decimal places.) to

Explanation / Answer

n1 =150 , p1 = 123/150 = 0.82
n2 = 100 , p2 = 59/100 = 0.59

z value at 90% = 1.645

CI = ( p1 - p2) +/- z * sqrt(p1 *(1 -p1) / n1 + p2 * (1 -p2)/n2)
= (0.82 - 0.59) +/- 1.645 * sqrt(0.82 * 0.18/150 + 0.59 * 0.41/100)
= (0.134 , 0.326 )
Lower Bound = 0.134
Upper Bound = 0.326

,

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