Question

# For our survey of Stat 281 students, there are 119 out of 318 students from the...

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.

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)

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