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The management of White Industries is considering a new method of assembling its golf cart. The present method requires a mean time of 42.3 minutes to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the 0.10 level of significance, can we conclude that the assembly time using the new method is faster?

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Answer:

At 0.10 significance level, there is significant evidence that the assembly time using the new method is faster

Step-by-step explanation:

Let mu be the true mean assembly time using the new method. Then hypotheses are:

[tex]H_{0}:[/tex] mu = 42.3 min

[tex]H_{a}:[/tex] mu < 42.3 min

Test statistic can be found using the equation:

t=[tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where

  • X  is the  sample mean assembly time (40.6 min)
  • M is the mean assembly time using the present method (42.3)  
  • s is the sample standard deviation (2.7 min)
  • N is the sample size (24)

Then t=[tex]\frac{40.6-42.3}{\frac{2.7}{\sqrt{24} } }[/tex] ≈ −3,08

one tailed critical t-score of 0.10 significance level with 23 degrees of freedom is ≈ 1.319

Since −3,08<--1.319, we can reject the null hypothesis.

Thus, we can conclude that the assembly time using the new method is faster

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