MHB How Is the Sampling Distribution of a Sample Mean Determined?

  • Thread starter Thread starter CGuthrie91
  • Start date Start date
  • Tags Tags
    Mean Sampling
AI Thread Summary
The sampling distribution of a sample mean is determined using the formula $$\bar{x}\sim N\left(\mu,\frac{\sigma}{\sqrt{n}}\right)$$ when the population standard deviation is known. In cases where the population mean and standard deviation are unknown, the sample mean can be approximated with $$\bar{x}$$, and the student-$t$ distribution should be used instead of the normal distribution. Understanding these concepts is crucial for solving related problems effectively. The discussion emphasizes the importance of knowing whether the population parameters are available for accurate calculations. Mastery of these principles is essential for tackling sampling distribution questions.
CGuthrie91
Messages
9
Reaction score
0
1. On this question I really have no idea how they got these answers so I just need someone to walk me through it step by step please

View attachment 42052. Part B on this question I don't know how to get the correct answer either

View attachment 4206
 

Attachments

  • Statistic question 1.PNG
    Statistic question 1.PNG
    6.5 KB · Views: 92
  • Statistic question 2.PNG
    Statistic question 2.PNG
    8.7 KB · Views: 80
Mathematics news on Phys.org
In your first problem, you're talking about the samping distribution of the mean. If the standard deviation of the population is known, you can use the normal distribution; that is,
$$\bar{x}\sim N\left(\mu,\frac{\sigma}{\sqrt{n}}\right),$$
where $\mu$ is as given, $\sigma$ is the population standard deviation (also given in this case), and $n$ is the sample size. As a side note: in most real-world applications, you don't know $\mu$ or $\sigma$. Not knowing the mean isn't such a big deal - just approximate with $\bar{x}$. But if you don't know $\sigma$, then you have to use the student-$t$ distributions instead of the normal distribution.

So, now that you know the sampling distribution, can you work out the rest of the problem?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top