A new design for the braking system on a certain type of car has been proposed.

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 122 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. Suppose braking distance for the new system is normally distributed with alpha = 12. Let denote the sample average braking distance for a random sample of 34 observations. What is the significance level for the rejection region R: {: LE 116.52}? How would you change the region to obtain a test with a = 0.05 R: {: LE }For the rejection region in part (a),what is the probability that the new design is not implemented when its true average braking distance is actually 115 ft?

Explanation / Answer

a)

P( z < (116.52 - 112 ) / ( 12 / srqt 34 ) )

P( z < 2.20 ) = 1 - 0.0139 = 0.9861

alpha = 0.0139

b)

z = 1.64

1.64 = ( x - 122 ) / ( 12 / srqt 34 )

x = 125.375

c)

P( z> 115 - 122 / (12 / srqt 34 ))

P z> -3.40) = 1 - 0.00034 = 0.99966

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.