Question

For our survey of Stat 281 students, there are 119 out of 318 students from the College of Agriculture & Biological sciences.

a. Calculate the sampling proportion p that are from College of Agriculture & Biological Sciences, then find out what is the standard error of p and the sampling distribution for p approximately normal?

b. Calculate a 95% confidence interval for proportion of students who are in the College of agriculture and Biological sciences in your stats class. then interpret the confidence interval.

Answer 1

a)

sample proportion, = 0.3742
sample size, n = 318
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.3742 * (1 - 0.3742)/318) = 0.0271

b)

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0271
ME = 0.0531

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.3742 - 1.96 * 0.0271 , 0.3742 + 1.96 * 0.0271)
CI = (0.3211 , 0.4273)

we are 95% confident taht the proportion of students who are in the College of agriculture and Biological sciences in your stats class is between (0.3211 , 0.4273)