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

its 50 miles away from the starting point