Question

The principal of a large high school wants to estimate the proportion of students who skip more than 10 days of school in a year.

A random sample of 100 students from a population of 1800 showed that 8 students skipped more than 10 days of school last year.

The upper limit (to four decimal places) of a 95% confidence interval for the proportion of students who skip more than 10 days of school in a year is

Answer 1

Denote :

x : Number of students in a sample skip more than 10 days of school in a year.

p = Sample proportion .

P = Population proportion .

N = Population Size.

n = Sample Size .

= Level Of Significance .

Here ,

N=1800

n=100

= 0.05

Now the formula for calculating upper limit is ,

For , = 0.05 ,

Putting All the value in above formula of Upper limit we get,

( Rounded off upto 4 decimal places )

The upper limit (to four decimal places) of a 95% confidence interval for the proportion of students who skip more than 10 days of school in a year is 0.1319 .

(For extra understanding , There will be atmost  13 students in the school who skip more than 10 days of school in a year .)