It is advertised that the average braking distance for a small car traveling at

Question

It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 37 small cars at 120 miles per hour and records the braking distance. The sample average braking distance is computed as 111 feet. Assume that the population standard deviation is 24 feet.

a. State the null and the alternative hypotheses for the test.

b. Calculate the value of the test statistic and the p-value.

c. The p-value is:

d. Use = 0.05 to determine if the average breaking distance differs from 120 feet.

e. Repeat the test with the critical value approach.

Explanation / Answer

Solution:

Set Up Hypothesis
Null Hypothesis H0: U=120
Alternate Hypothesis H1: U!=120
Test Statistic
Population Mean(U)=120
Given That X(Mean)=111
Standard Deviation(S.D)=24
Number (n)=37
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=111-120/(24/Sqrt(37))
Zo =-2.2810
| Zo | = 2.2810
Critical Value
The Value of |Z | at LOS 0.05 is 1.64
We got |Zo| =2.2810 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -2.2810 ) = 0.0225
Hence Value of P0.1 < 0.0225, Here We Do not Reject Ho

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

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