SOLUTION: Hello, please i need help with this question. In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances,

Algebra ->  Probability-and-statistics -> SOLUTION: Hello, please i need help with this question. In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances,       Log On


   

Question 1201156: Hello, please i need help with this question. In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained:
Specimen: 1,2,3,4,5,6.
A: 10.16,10.88,10.49,5.29,8.25,7.58
B: 10.17,10.87,10.48,5.28,8.26,7.54
State the null and alternate hypotheses.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

I'll provide the answers first at the top of the page.
The next section will do a deeper dive explaining things.

Answers:
  • null hypothesis aka
  • alternate hypothesis aka
mu = mu is used for the population mean.
========================================================================

Explanation:

Standard practice with population parameters generally involves Greek letters.
Examples:
  • Greek letter mu = mu = population mean
  • Greek letter sigma = sigma = population standard deviation
  • Greek letter rho = rho = population correlation coefficient
and so on. We use the lowercase version of each letter.

The one exception to this rule, that I can think of anyway, is the use of 'p' for the population proportion (the sample version is phat).

We're looking at the mean weights so we go for mu or mu.
Both "mean" and "mu" start with M, which is one way to remember the connection.

If we want to talk about two (or more) different population means, it's common to attach a number to the bottom right corner of this variable.
  • mu1 = mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2C1%29%5D = population mean of group 1
  • mu2 = mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2C2%29%5D = population mean of group 2
  • etc
Some textbooks will use letters instead of numbers.
  • muA = mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CA%29%5D = population mean of group A
  • muB = matrix%281%2C2%2C%22%22%2Cmu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D%29 = population mean of group B
  • etc
To be even more descriptive, the letters can be replaced with short names.
Examples:
  • mu_dogs = mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2Cdogs%29%5D = population mean of dogs' weight
  • mu_cats = mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2Ccats%29%5D = population mean of cats' weight
It will depend on context which is the better format.
Statistical software like Minitab often uses a format similar to the last set of examples shown above.

Since your teacher is involving letters, I'll go for that style.

------------------

The instructions mention "In an experiment to determine whether there is a systematic difference between the weights"
Meaning that the researcher wants to test the claim if is the case or not.
The flip of that statement would be

For each statement, we can optionally subtract mu%5Bmatrix%281%2C3%2C%22%22%2C%22%22%2CB%29%5D from both sides.
Eg: becomes

Why do we bother with this subtraction? It's to conduct a hypothesis test on the difference of the population means.
Treat that difference as a new random variable on its own.

Rule: The null hypothesis ALWAYS has the equal sign.
This is to lock the parameter(s) into one spot and set up one distribution.

Therefore,
  • null hypothesis aka
  • alternate hypothesis aka
This is a two-tailed test because of the "not equals" in the alternate/alternative hypothesis.

I'll stop here since it seems like all you need are the null and alternate hypotheses.
Let me know if have further questions. Or please make a new post on this website.