Question

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student.

Construct a 95% Confidence Interval for the true mean age of Winter Foothill College students by working out then answering the exercise.

How much area is in both tails (combined)? (Enter an exact number as an integer, fraction, or decimal.)

α =

Answer 1

Solution:

Given:
The population standard deviation =

Sample size = n = 25

Sample mean =

We have to construct a 95% Confidence Interval for the true mean age of Winter Foothill College students.

Formula:

where

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

Thus

We are 95% confident that the true mean age of Winter Foothill College students is between 24.52 and 36.28.

How much area is in both tails (combined)?

Area is in both tails =

Area is in both tails =

Area is in both tails =