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.

(b) Suppose braking distance for the new system is normally distributed with σ = 11. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to H₀ than 117.2?

What is the P-value in this case? (Round your answer to four decimal places.)

Answer 1

Test is left tailed. The rejection region is

The values of x that are less than 117.2 are more contradictory to H₀ than 117.2.

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Decision: Since p-value is less than 0.05 so we reject the null hypothesis.