Question

Here are the results of computer readings from a vehicle whose cruise control is set to 60mph.

37.2 19.0   21.0 26.1 17.4 25.8 24.9 41.4 27.0 34.4

36.9 32.5 38.8 25.3 35.3 26.5 32.3 28.2 23.9 22.1

Suppose the standard deviation for the population is known to be 6.5 mpg

A) Find a 95% confidence interval for u, the (population) mean mpg for this vehicle.

B) Find a 99% confidence interval for u, the (population) mean mpg for this vehicle.

Answer 1

= (37.2 + 19 + 21 + 26.1 + 17.4 + 25.8 + 24.9 + 41.4 + 27 + 34.4 + 36.9 + 32.5 + 38.8 + 25.3 + 35.3 + 26.5 + 32.3 + 28.2 + 23.9 + 22.1)/20 = 28.8

A) At 95% confidence interval the critical value is z^* = 1.96

The 95% confidence interval for is

+/- z^* *

= 28.8 +/- 1.96 * 6.5/

= 28.8 +/- 2.85

= 25.95, 31.65

B) At 99% confidence interval the critical value is z^* = 2.58

The 99% confidence interval for is

+/- z^* *

= 28.8 +/- 2.58 * 6.5/

= 28.8 +/- 3.75

= 25.05, 32.55