Question

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)

Answer 1

Answer:

Null hypothesis:$\mu \geq 42.3$  

Alternative hypothesis:$\mu < 42.3$  

$t=\frac{40.6-42.3}{\frac{2.7}{\sqrt{24}}}=-3.085$    

The degrees of freedom are given by:

$df=n-1=24-1=23$  

Then the p value can be calculated with this probability:

$p_v =P(t_{(23)}<-3.085)=0.0026$  

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

$\bar X=40.6$ represent the sample mean for the new method

$s=2.7$ represent the sample standard deviation

$n=24$ sample size  

$\mu_o =42.3$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ 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:$\mu \geq 42.3$  

Alternative hypothesis:$\mu < 42.3$  

The statistic for this case is given:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$  (1)  

The statistic would be given by:

$t=\frac{40.6-42.3}{\frac{2.7}{\sqrt{24}}}=-3.085$    

The degrees of freedom are given by:

$df=n-1=24-1=23$  

Then the p value can be calculated with this probability:

$p_v =P(t_{(23)}<-3.085)=0.0026$  

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