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 70 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 21 feet. (You may find it useful to reference the appropriate table: z table or t table)

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

• H₀: μ = 120; H_A: μ ≠ 120

• H₀: μ ≥ 120; H_A: μ < 120

• H₀: μ ≤ 120; H_A: μ > 120

b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

Find the p-value.
  

• 0.01

  

  p-value < 0.025
• 0.025

  

  p-value < 0.05
• 0.05

  

  p-value < 0.10
• p-value

  

  0.10

• p-value < 0.01

c. Use α = 0.10 to determine if the average breaking distance differs from 120 feet.
  

Answer 1

Solution :

$\mu$= 120

$\bar x$ = 111

$\sigma$ =21

n = 37

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 120

H_a : $\mu$   $\neq$ 120

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (111-120) / 21 / $\sqrt$ 37

= -2.61

P (Z < -2.61 ) = 0.0091

P-value = 0.01

$\alpha$ = 0.10

p=0.01< 0.10

Reject the null hypothesis .

There is enough evidence to claim that the population mean μ is different than 120, at the 0.10 significance level.