Question

8. a) A random sample of n=300 observztions from a binomial population produced x=263 sucesses. Find a 90% confidence interval for p.

b) Ten randomly selected lobsters were caught in the sea. The measured : 78, 66, 65, 63, 60, 60, 58, 56, 52, 50 mm's. Find a 95% confidence interval.

Answer 1

a) From standard normal tables, we get here:

P( -1.645 < Z < 1.645 ) = 0.9

The sample proportion here is computed as: p = 263/300 = 0.8767

Therefore the confidence interval here is computed as:

This is the required confidence interval here.

b) The sample mean and sample standard deviation here are first computed using the following table as:

The sample mean here is computed as:

Now the sample standard deviation is computed as ( from last column )

For n - 1 = 9 degrees of freedom, we get from the t distribution tables:

P( -2.262 < t₉ < 2.262 )= 0.95

The confidence interval here is obtained as:

This is the required confidence interval here.