Question

A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design.

Let μ = true average braking distance for the new design at 40 mph. The hypotheses are: H₀: μ = 120 vs. H_a: μ ≠ 120.

Suppose braking distance for the new system is normally distributed with σ=10. Let X-bar denote the sample average braking distance for a random sample of 36 observations. What is the P-value for X-bar = 117.2?

Apparently is not 0.0633 or 0.0465

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 120

H_a : 120

Test statistic = z

= ( - ) /    / n

= (117.2 - 120) / 10 / 36

= -1.68

Test statistic = -1.68

P-value = 0.093