Question 1187179
population mean = 35 minutes.
sample size = 13
sample mean = 33.3 minutes
standard deviation of sample = 2.4 minutes
significance level = 5%.


use of t-score is indicated.
here's a reference.
<a href = "https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value" target= "_blank">https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value</a>


standard error = sample standard deviation / square root of sample size = 2.4 / sqrt(13) = .6656402355


t-score = (x - m) / s = (33.3 - 35) / .6656402355 =  -2.553932153.


critical t-score at one-tailed 5% significance level with 12 degrees of freedom = -1.782287494.


since the test t-score is greater than that, the results are significant, indicating there is good reason to believe that the certain modification would reduce the average time of the car manufacturing process.


H0 (the existing process) is rejected in favor of Ha (the alternate process).


here's a good t-test calculator that you can use to check your results.


<a href = "https://mathcracker.com/t-test-for-one-mean#results" target = "_blank">https://mathcracker.com/t-test-for-one-mean#results</a>


if you have trouble using this calculator, let me know and i'll guide you through it.


you should be able to duplicate the results i gave you, using this calculator.


theo