We want to know what percentage of the population have college degrees. We take a sample of 100 individuals and find that 28 have college degrees. Answer the following, rounding your answers to 2 decimal places. a. What is the sample proportion? b. Find the SE. c. Construct a 95% confidence interval. d. What does this 95% confidence interval tell us about our population proportion p? (One sentence is the perfect length for an answer)

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jtellezd jtellezd · Answer 1 · 2021-06-24T03:30:43+02:00

Answer:

a) p = 28/100 p = 0,28 or p = 28%

b) SE = 0,0448

c) CI 95 % = ( 0.1921 ; 0.368 )

We can support with 95 % of confidence that the proportion of people with a College degree would be found within these limits

Step-by-step explanation:

a) Sample proportion: Is the number of positive success divide by sample size

That is from 100 ( individuals) ( sample size ) it was found that 28 had College degree ( positive success)

Then p = 28/100 p = 0,28 or p = 28%

b) The standard error is

SE = (√p*q)/n

p = 0,28 then q = 1 - 0,28 q = 0,72

SE = √ (0.28)*(0.72)/100

SE = √0.002016

SE = 0,0448

c) CI = 95 % then significance level is α = 5 % α = 0.05

α/2 = 0.025

From z- table we find z(c) = 1.96

Then CI 95 % = p₀ ± z(c) * SE

CI 95 % = 0.28 ± 1.96*0.0448

CI 95 % = ( 0.28 ± 0.088 )

CI 95 % = ( 0.1921 ; 0.368 )

d) We can support with 95 % of confidence that the proportion of people with college degree would be found within these limits