Confidence Interval


If the population variance is unknown, it can be estimated using:
σ² = (1 / (n-1) ) ( Σx² - (Σx)² / n )

Exercises for students
Solve the following problems on paper and check your working using the above applet:

In an investigation into the weight of school children, 100 randomly chosen children were weighed.
The sample mean was found to be 50 kg, and the standard deviation was 2 kg.
Calculate a 95% confidence interval for the population mean weight of children.


In a survey into things that people fear, 43 people out of a random sample of 100 people said they were afraid of spiders.
Find a 90% confidence interval for the proportion of the population who are afraid of spiders.

Summary
The α% confidence interval for the population mean µ is ( sample mean ± z σ / sqrt(n) )
The α% confidence interval for the population proportion p is ( p_s ± z sqrt( p_sq_s / n ) )
where P(Z < z) = α + (1 - α) / 2
p_s = sample proportion





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