For EACH of the 2 majors, consider the 'School Type' column. Construct a 90% confidence interval for the proportion of the schools that are 'Private'.
Please see attached
Confidence Interval:
The form of the confidence interval is,
CI = Point estimate ± Margin of error
The approximate 100*(1–α)% confidence interval for the population proportion will be obtained using the formula given below:
Obtain the sample proportion of the schools that are private:
It is given that among a sample of 20 schools, 16 schools are private schools.
The sample size is n = 20.
The number of specified characteristics is x = 16.
The sample proportion of the schools that are private is obtained as 0.8 from the calculation given below:
p^ = x/n
= 16/20
= 0.8.
Obtain the critical value:
The given confidence level is 100*(1–α)% = 90%.
From this, the level of significance value is α = 0.1.
The critical value corresponding to the 90% confidence level is obtained as z(α/2) = ±1.645 from the calculation given below:
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