MHB Chloe's question via email about a p-value

  • Thread starter Thread starter Prove It
  • Start date Start date
  • Tags Tags
    Email P-value
AI Thread Summary
The discussion centers on calculating the p-value for a hypothesis test with null hypothesis H0: μ = 13 and alternative hypothesis Ha: μ < 13, using provided data. The test statistic is calculated as approximately -0.253, leading to an initial p-value estimate of about 0.401. A more precise p-value obtained through technology is approximately 0.399948, confirming the accuracy of the initial approximation. The conversation highlights the importance of using both manual calculations and technology for statistical analysis. Overall, the calculations demonstrate a solid understanding of hypothesis testing and p-value determination.
Prove It
Gold Member
MHB
Messages
1,434
Reaction score
20
pvalue.png

I'm assuming the hypothesis test is

$\displaystyle H_0 : \mu = 13 \quad \quad H_a : \mu < 13 $

We are given $\displaystyle \mu = 13, \quad \sigma = 2.47, \quad \bar{x} = 12.86 , \quad n = 20 $.

The test statistic is

$\displaystyle \begin{align*} z &= \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \\
&= \frac{12.86 - 13}{\frac{2.47}{\sqrt{20}}} \\
&\approx -0.253\,481 \end{align*} $

Thus the p value is

$\displaystyle \begin{align*} p &= \textrm{Pr}\left( Z < -0.253\,481 \right) \\
&\approx \Phi \left( -0.25 \right) \textrm{ from the Z distribution table}\\
&= 0.401\,29 \end{align*} $

However, a CAS (or Linear Interpolation) could be used to get a more accurate value. Using technology, I find the p value to be $\displaystyle 0.399\,948 $, which our approximation is very close to.
 
Last edited by a moderator:
Mathematics news on Phys.org
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

Similar threads

Back
Top