Calculate a 90% confidence interval. There's a report saying that 67% of teachers surveyed think that computers are now essential tools in the classroom. Suppose that this information was based on a random sample of n=200 teachers.

geneth1u

geneth1u

Answered question

2022-09-11

Calculate a 90% confidence interval
There's a report saying that 67% of teachers surveyed think that computers are now essential tools in the classroom. Suppose that this information was based on a random sample of n = 200 teachers.
Calculate a 90% confidence interval for π, the true proportion of teachers who think the computer is essential in the classroom.
I know how to find the confidence interval for mean, variance and s.d., but I'm not sure of how to calculate the confidence interval for π, can anyone give me a hand and show me how it works please?

Answer & Explanation

Sharon Dawson

Sharon Dawson

Beginner2022-09-12Added 20 answers

Step 1
Let X i = 1 if teacher i think that computers are now essential tools, X i = 0  otherwise otherwise.
Step 2
You have: X i are independant with the same distribution E X i = π and V a r X I = π ( 1 π ).
Then use both mean and sd estimates, and the Central Limit Theorem to compute the confidence interval.
nar6jetaime86

nar6jetaime86

Beginner2022-09-13Added 2 answers

Step 1
Let p = sample proportion, and q = 1 p , and n = sample size. Also critical value z = 1.65 for the 90% C.I. First compute the error E = z ( p q / n ) 1 / 2 = 1.65 ( .67 .33 / 200 ) 1 / 2 = 0.054.
Step 2
Thus the C . I = ( p E , p + E ) = ( .67 .054 , .67 + .054 ) = ( .616 , .724 ) .

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