The management of ABC Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, 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 a 0.1 level of significance, can we conclude that the assembly time using the new method is faster? Use only the P-Value approach. State H0 and Ha (20 pts)

Null hypothesis:  

Alternative hypothesis:  

The degrees of freedom are given by:

Then the p value can be calculated with this probability:

If we compare the p value and the significance lvel of 0.1 we see that the p value is lower than the signficance level we can reject the null hypothesis and we can conclude that the the assembly time using the new method is faster

Step-by-step explanation:

Information given

represent the sample mean for the new method

represent the sample standard deviation

sample size  

represent the value that we want to test

represent the significance level

t would represent the statistic

represent the p value

System of hypothesis

We want to verify if  the assembly time using the new method is faster, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic for this case is given:

 (1)  

The statistic would be given by:

The degrees of freedom are given by:

Then the p value can be calculated with this probability:

If we compare the p value and the significance lvel of 0.1 we see that the p value is lower than the signficance level we can reject the null hypothesis and we can conclude that the the assembly time using the new method is faster