Question

1. A random sample of 240 students were asked “Do you buy your books from the UP bookstore?” and 42% said “yes”.
   1. Construct a 90% confidence interval for the true population proportion (p) of students who buy their books at the UP bookstore.

2. Interpret your answer:

Answer 1

a)

Let p denotes the population proportion. Let o denotes the sample proportion and n denotes the sample size. Here, p = 0.420, n = 240, standard error 0.420 * (1 – 0.420) 240 = 0.031859 0.0319 At 90 percent confidence level, Margin of error is p* (1 - e) ME= * 21-0.9 0.420 * (1 – 0.420) 240 * 20.05 = 0.420 * (1 – 0.420) 240 * 1.644854 = 0.052403 ~ 0.052 n a 90 percent confidence interval for the population proportion p is p = (1-p) = P + * 2 1-0.9 n = 0.4200 + 0.420 * (1 – 0.420) 240 * 20.05 = 0.4200 + 0.420 * (1 – 0.420) * 1.644854 240 = 0.4200 + 0.052403 = - (0.367597,0.472403) ~ (0.368,0.472)

b) Interpretation : Out of 100 samples drawn, sample proportion will be between (0.368, 0.472) for 90 samples.