University:
York University
Course:
MATH 1131 | Introduction to Statistics I
Academic year:

2022
Views:

389

Pages:

2
Author:

Niklas

LECTURE 27 Cl for the mean (d' unknown). We estimated with its unbiased sample variance, S (x- χ-μ 11-4 メ-μ we replace / that we cauwot evaluate, with 5/ that does NOT follow a Normal distribution, but a Student & with n-d degrees of freedom メーμ 5/ Ntn- From that we know: S -1-0 Student t-sled The student & distribution has been introduced by William Gosset, in charge of the brewing for the Guinness to Investigate the quality of beer productions comparing beer samples The Student with ne degrees of freedom, (, has probability density function (x)- it is bell shaped as the Normal distribution, lowever the smaller the degrees of freedom in the heavier its tails Differently from the normal distribution table, the Studont table indicates the quantiles for different probability leals On the now we hain the degreat of freedon On the column we have the probabiicies order of a Student with & degrees of freedom Example 1=19, P=0.995 t=2.86 0.995 Example CI for the proportionm ~位) Final formula for the confidence interval for the proportion From the CI to data example 1 Assume you extracted a sample for a proportion and a confidence interval of level 95% with bounds 227 and 8491 has been obrved, find and the sample se Since we are dealing with a proportion, the formuls we have to refer to the interval is centered around 2, thun (0.227-0493)=0.30 To find the sample size we can noter that 0.493 6.227 0.206 10361 0.36) 0.48 2x1.96 2x196 0266 797 49.9949 (1 (1 1/2 From the CI to dato example 2 Assume you extracted a sample from a normal population with known varlancs and the Clat 95% far the moon has bounds 9.100 and 10.60. Find and the sample varance Since its moar, the formesls we have to refer to the Cl is entered areand ji, thus (08)-10.29 We can't find the sample size, indeed 21063-9.398 0.782 From which 0782 2 0.1995 00398 From the CI to data: example 3 Assume you tracte a samps of she wow 10 from a sarmal population an the for the mean bas bonik 626 and 12.52. Whatanias Since it is men, the Toimul we have to refer t Example body temperature. What Home boy gaan? shained a normal timperatum of 57ンイ 1992 a mondhury was shame to the củi cũng of the per To find wrce 241252-926-1.25 Thus 3 35 2.279525.193 22.262 Example: newborn Dala are relates to the FVG sleen we fuve 6511 19337 0501 05/1 The table below shows the CI for the probability that a male will be born, computed using the samples of Muggia FVG and lialy CI 98% CI 95% 38 85 0.447 0.053900 9.341 0.553 0.306 0.586 5286 10337 0.511 0.004920 0.501 0.521 0498 0.524 289185 551944 0.515 0.000667 0.514 0.536 0513 0.517 the