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

Null hypothesis:
`\mu \geq 42.3`

Alternative hypothesis:
`\mu < 42.3`

`t=(40.6-42.3)/((2.7)/(√(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

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=(\bar X-\mu_o)/((s)/(√(n)))` (1)

The statistic would be given by:

`t=(40.6-42.3)/((2.7)/(√(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