Alathe is set to cut bars of steel into lengths of 6 centimeters. the lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. a sample of 144 bars is selected randomly and measured. it is determined that the average length of the bars in the sample is 6.09 centimeters with a standard deviation of .48 centimeters.

a. formulate the hypotheses to determine whether or not the lathe is in perfect adjustment.

b. compute the test statistic.

c. using the p-value approach, what is your conclusion? let ? = .05.

how do you compute using excel?

  We reject    H₀             ⇒   μ₀  = 6

Step-by-step explanation:

We are going to evaluate in a two tail test (the lathe cut above or below 6 ?)

So:

Normal Distribution with mean μ₀ = 6  and Standard deviation σ = 0.48

1.- Hipothesis test:

Null hypothesis                           H₀             ⇒   μ₀  = 6

Alternative hypothesis               Hₐ             ⇒   μ₀  ≠ 6

To compute the z(s)  we apply :

z(s) = [ ( μ  -   μ₀) ] / (σ√144)            ⇒  z(s) = [ ( 0.09 )* 12 ]/ .48

z(s) = 2.25

Now we have to compare z(s)   with  z(c) and we find z(c) from tables taken into account that   α = 0.05  or the confidence interval is 95 %

and as the test is a two tail one we get haft of α for each tail.

So we have to find the value of z(c) from an area value of 0.025

then  z(c) = 1.96

Then we have the situation in which z(s) > z(c)    2.25 > 1.96 that means we are in the rejection zone so we reject null hypothesis

Using excel we in any cell we do as follows

In a cell we insert fucntion and look for statistics and standard normal distribution

we introduce values of z(s) and we will get the probability of z(s) = .987 that probability is out of 0.95 the requierement of the problem so we reject       H₀             ⇒   μ₀  = 6

We also can use inverse normal distribution. In which case we must introduce areas (for instance 0,05) to find the z(c) and the compare

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.