Question

The average height of 49 randomly selected men is 175 cm with σ = 7.
When calculating a 95% confidence interval. The point estimate would be? The critical value? The standard error? The margin of error?

Answer 1

Solution:

Sample Size = n= 49

Sample Mean =

Population Standard Deviation =

Confidence level = c = 95% = 0.95

Part a) The point estimate :

Sample mean is the point estimate of population mean,

thus point estimate is:  

Part b) The critical value:

Z value for 95% confidence level:

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Part c) The standard error

Part d) The margin of error

Thus 95% confidence interval would be: