# Statistics - Sample Mean

• Mar 3rd 2014, 03:03 PM
AwesomeHedgehog
Statistics - Sample Mean
To determine whether a metal lathe that produces machine bearings is
properly adjusted, a random sample of 25 bearings is collected and the
diameter of each is measured. The metal lathe has a historical standard
deviation of 0.015 for the diameter of the machine bearings.

a.) The sample mean, YBAR, of the 25 bearings will be calculated.

What is the probability that the sample mean, YBAR,
will be within 0.0075 of the metal lathe's true mean diameter, mu,
for the bearings being produced?

What did you assume in order to calculate this probability?

b.) The following random sample of 25 bearing diameters was obtained.

1.003 1.012 0.990 1.025 1.005
0.989 0.979 1.024 0.998 1.006
0.985 0.998 0.978 0.992 0.982
1.015 1.002 1.018 0.977 1.001
0.994 1.007 1.018 1.027 1.024

Calculate the following SAMPLE statistics:
mean, variance, standard deviation, and range.

How comfortable are you with your assumptions from part (a)?

c.) The target diameter of the bearings being produced is 1.

Using your answers from parts [(a and b)] to guide your logic,
do you believe the metal lathe is properly adjusted? Justify Your Answer.

This is what I have so far and I am just wondering if it is correct and how to continue onto part c:

a) z = ( x - μ ) / (σ÷√η) = -2.5

z = ( x - μ ) / (σ÷√η) = 2.5
P (0.9925 < x < 1.0075) = P (-2.5 < z < 2.5) = 0.9876

b) n= 25; Σx= 25.049; Σx²= 25.104; Σx³= 25.165; Σx^4= 25.232
Mean(μ)= 1.002; median= 1.0025; No Mode
σn-1 = 0.0157; (σn-1)²= 0.0002; CV% = 1.6%
range= 0.05; mid-range= 1.002; Probably right skewed.
Five number summary: Q0= 0.9775, Q1= 0.99, Q2= 1.0025, Q3= 1.018, Q4= 1.027, IQR= 0.028
Inner fence: 0.948 to 1.06, Outer fence: 0.906 to 1.102

• Mar 4th 2014, 04:28 AM
romsek
Re: Statistics - Sample Mean
how did you generate this? Do you have a program of some sort? It seems unlikely to me that you typed all this in by hand including all the items the problem doesn't ask for.

a) is correct
b) all your numbers are correct which is to be expected for software.

so yeah, you're ready to go to (c)
• Mar 4th 2014, 05:50 AM
AwesomeHedgehog
Re: Statistics - Sample Mean
I used the program, Minitab, to help me solve the problem. I was just wondering if it seemed to be correct.
• Mar 4th 2014, 06:07 AM
AwesomeHedgehog
Re: Statistics - Sample Mean
For part c, I'm wondering if I am wording this correctly.

In part a, I got the P(-2.5 < z < 2.5) = 0.9876, meaning that there is a high probability that the sample mean will be within 0.0075 the metal lathe's mean diameter. Then from part b, I got the mean, variance, standard deviation, and range and those values helped support my assumption in part a that P(-2.5 < z < 2.5) = 0.9876.

So, for part c, would it be wrong for me to say that I believe that the metal lathe is properly adjusted?
• Mar 4th 2014, 01:02 PM
romsek
Re: Statistics - Sample Mean
Quote:

Originally Posted by AwesomeHedgehog
For part c, I'm wondering if I am wording this correctly.

In part a, I got the P(-2.5 < z < 2.5) = 0.9876, meaning that there is a high probability that the sample mean will be within 0.0075 the metal lathe's mean diameter. Then from part b, I got the mean, variance, standard deviation, and range and those values helped support my assumption in part a that P(-2.5 < z < 2.5) = 0.9876.

So, for part c, would it be wrong for me to say that I believe that the metal lathe is properly adjusted?

It's been ages since I looked at this but I'd guess this is a hypothesis test question.

H0: The lathe is properly adjusted
H1: The lathe is improperly adjusted

There must be something in your text that describes how to use these statistics to test one hypothesis vs. the other
• Mar 4th 2014, 03:03 PM
AwesomeHedgehog
Re: Statistics - Sample Mean
Honestly, I looked at the book and for the Chapters that this assignment is covering, there is nothing about that in the book. Plus my teacher never went over anything like this in class. So, for part c, I just wrote down what I believed, tried to use logic based on parts (a) and (b). Hopefully I am correct.