Question

(COMPUTE AND INTERPRET CONFIDENCE INTERVAL ESTIMATES)

A college admissions officer sampled 120 entering freshmen and found that 42 of them scored more than 550 on the math SAT. Construct a 99% confidence interval for the proportion of all entering freshmen at this college who scored more than 550 on the math SAT. Find the critical values, find E , the margin of error, then compute and interpret your interval estimate with a full sentence.

Critical value: (draw, label & shade)

Margin of error, E :   

Confidence Interval:

Answer 1

Given: n=120, x=42 ... The sample proportion is, ___ p=X=42 = 0.35 0 120 The significancel tevel =2=0.01 O critical rouue : L = 70.01 = 12:58 -co . La 230_la @ The margin of error is, . Eslg lg : 9=1-p 2 vn = 2.58 0.35 X0.65 = 0.1123 120 4) The 99% confidence interval for the proportion of all entering freshmen at this college who scored more than sso on the math SAT is, ÞIba pa 2 1 0 8.35 10.1123 0.2379 <p 3 0.4623__

Interpretation. We estimate with 99% confidence that the true proportion of all entering freshmen at this college who scored more than sso on the math SAT Lis: between 0.23719 = 23:9717. Cind 0.4623 = 46.23%