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Answer: a. The interval in percentage is (23.46% , 30.76%)
b. No
Step-by-step explanation: To determine the confidence interval of a proportion, first find the percentage of yellow in that population:
phat =
phat = 0.2711
The level α is 95%
1 - α = 0.05
α/2 = 0.025
As the population is bigger than 30, use z-test.
According to the table, z-score for α/2 = 0.025 is z = 1.96
The error for the interval is:
E = z.
E = 1.96.
E = 1.96*0.01865
E = 0.0365
The lower and higher limits of the interval are:
phat - E = 0.2711 - 0.0365 = 23.46%
phat + E = 0.2711 + 0.0365 = 30.76%
In conclusion, the 95% confidence interval to estimate the percentage of yellow is (23.46%,30.76%)
b. No, because 25% is inside the interval meaning that it doesn't contradict the expectations.