We are interested in estimating the proportion of people that could not identify

Question

We are interested in estimating the proportion of people that could not identify neither Nebraska nor Vermont. In a class of 55 students, each student was requested to select a sample of 6 people, show each person a map of the US and ask the person to identify the states of Vermont and Nebraska. The following numbers are the counts that each student got, that is, each number is the count of people in the student sample of 6, that could not identify Nebraska nor Vermont.  

Note: You can cut and past these numbers into an excel spread sheet to help you with the calculations and compute the confidence interval.

When we callect all the students' data, we have a sample size of 6x55=330.

Of the sample of 330 people, what proportion were not able to locate either state? ____ Round answers to 4 decimals.

Find a 95% confidence interval for the true proportion of people that cannot locate Nebraska nor Vermont.

The 95% confidence interval is (____,____) Round answers to 2 decimals.

3 1 1 0 2 1 0 1 1 1 2 1 2 0 0 0 1 3 0 2 2 0 1 6 1 1 2 4 3 1 0 2 2 1 1 1 0 3 0 3 0 0 0 0 2 1 2 0 3 0 0 0 3 1 0

Explanation / Answer

From the data, we get mean = 1.236

Standard deviation = 1.264

So proportion not able to locate either state = 1.236/ 6 = 0.2060

Standard deviation of proportion of people not able to identify either state = 1.264 / sqrt(6) = 0.516

alpha = 0.05

Z0.975 = 1.96

So, 95% CI is (mean - Z*std_dev, mean + Z*std_dev) = (0.2060 - 1.96*0.516, 0.2060 + 1.96*0.516) = (-0.81, 1.22)

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