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According to the National Center for Education Statistics, 13% of all public-school students, ages 3-21, receive...

According to the National Center for Education Statistics, 13% of all public-school students, ages 3-21, receive special education services. To validate these findings, a random sample of 300 students was asked if they receive special education services. A total of 54 students from this sample responded that they did. Which of the following statements is correct?

a The interval that contains 95% of the sample proportions is 0.092 and 0.168. Because the sample proportion is between these two values, we have support for the results of the National Center for Education Statistics.
b The interval that contains 95% of the sample proportions is 0.092 and 0.168. Because the sample proportion is not between these two values, we do not have support for the results of the National Center for Education Statistics
c The interval that contains 95% of the sample proportions is 0.064 and 0.196. Because the sample proportion is between these two values, we have support for the results of the National Center for Education Statistics.
d The interval that contains 95% of the sample proportions is 0.064 and 0.196. Because the sample proportion is not between these two values, we do not have support for the results of the National Center for Education Statistics.
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Answer #1

We have, = 0.13 n = 300

The 95% confidence interval of the population proportion is given by:

[, ] = [0.13 - 0.04, 0.13 + 0.0435] = [0.09, 0.17].

The interval that contains 95% of the sample proportions is 0.092 and 0.168. Because the sample proportion is between these two values, we have support for the results of the National Center for Education Statistics.

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