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.
H0: μ = 6; HA: μ ≠ 6
H0: μ ≥ 6; HA: μ < 6
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.
0.005 < p-value < 0.01
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
c. Use α = 0.05 to test if the new sports car is meeting its goal.
(Click to select)Reject H0Do not reject H0 . At the 5% level of significance, we (Click to select)cancannot conclude that the average clock time of all cars is less than 6 seconds.