Question 1187179: An economist for a certain car manufacturing process indicates that a car manufacturing process takes an approximate average time of 35 minutes. However, the economist believes that a certain modification would reduce this time, and after being modified, the process is repeated 13 times, giving an average time of 33.3 minutes with a standard deviation of 2.4 minutes. Determine if there is any significant reduction in time taken in the manufacturing process at 5% level of significance.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value
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.
https://mathcracker.com/t-test-for-one-mean#results
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
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