(Round all intermediate calculations to at least 4 decimal places.) A car manufacturer is trying to develop a new sports car.

(Round all intermediate calculations to at least 4 decimal places.)

A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The car company tested 12 of the cars and clocked their performance times. Three of the cars clocked in at 5.8 seconds, 5 cars at 5.9 seconds, 3 cars at 6.0 seconds, and 1 car at 6.1 seconds. At a 5% level of significance, test if the new sports car is meeting its goal to go from 0 to 60 miles per hour in less than 6 seconds. Assume a normal distribution for the analysis.

a.Specify the competing hypotheses to test this belief.  

a.)  H0: μ = 6; HA: μ ≠ 6

 b.) H0: μ ≥ 6; HA: μ < 6

 c.) H0: μ ≤ 6; HA: μ > 6 

b-1.Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

  Test statistic   __________

b-2.Select the p-value. 

a.)   0.005 < p-value < 0.01

b.) p-value < 0.01

c.) 0.01 ≤ p-value < 0.025

d.) 0.025 ≤ p-value < 0.05

e.) 0.05 ≤ p-value < 0.10

f.) p-value ≥ 0.10 

c.Use α = 0.05 to test if the new sports car is meeting its goal.

(Reject or Not Reject?) At the 5% level of significance, we (can or cannot?) conclude that the average clock time of all cars is less than 6 seconds.