Question

For some objects that are normally distributed, there is a variance 15 and unknown mean μ. In a simple random sample of 45 objects, the sample mean object was 16. Construct a symmetric 90% confidence interval forμ.

Answer 1

Solution

a) variance = 2 = 15

standard deviation = = 2 = 15 = 3.87

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 3.87 /  45 )

= 0.95

At 90% confidence interval estimate of the population mean is,

  ± E

= 16 ± 0.95

= ( 15.05, 16.95 )

b) variance = 2 = 9

standard deviation = = 2 = 9 = 3

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 3 /  36 )

= 0.82

At 90% confidence interval estimate of the population mean is,

  ± E

= 15 ± 0.82

= ( 14.18, 15.82 )