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

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4