Hypothesis Test: Pi = 3.2?
In the year 1897, legislature was introduced in Indiana that would make 3.2 the official value of pi for the State. Now, that sounds silly, however is it really?
Claim: Pi is 3.2.
To verify the claim, we are going to produce a whole bunch of values for pi, and then test to observe if the mean is 3.2.
H0: mu = 3.2 (that is, original claim)H1: mu <> 3.2 (that is, two tail test)
Procedure:
Area of the unit circle is pi. In first quadrant the area of unit circle is pi/4. The calculator produces random numbers between 0 and 1. What we are going to do is to generate two random numbers that will simulate a randomly selected point in a unit square in first quadrant. If the point is in the circle, then the distance from (0,0) will be less than or equivalent to 1, and if the point is outside the circle, then the distance will be more than 1.
Encompass the calculator producing a squared distance from zero (that is, the square of distance explains the similar properties as far as being less than 1 or more than 1). Repeat this 25 times. Each time, record whether the point is within the circle (<1) or outside the circle (>1).
RAND^2 + RAND^2
Pi/4 is around equivalent to the ratio of points within the circle to the total number of points. Thus, pi will be 4 times the ratio of points within the circle to total number of points.
This entire process is repeated many times, and the mean and standard deviation is recorded.The hypothesis test is then performed by using the t-test to see if the true mean is 3.2 (based on sample mean).
Illustration:
20 values for pi were produced by generating 25 pairs of arbitrary numbers and checking to see if they were within or outside the circle as explained above.
3.68 3.20 3.04 2.56 3.363.36 3.36 3.52 3.04 3.203.52 3.36 3.04 2.72 3.363.52 2.88 2.88 3.68 2.60
Mean of the sample is 3.194, that is, the standard deviation is 0.3384857923.
The test statistic t = (3.194 - 3.2)/(0.3384857293/sqrt(20)) = - 0.0792730931
The critical value, with 0.05 level of significance as none was stated, for a two-tail test by 19 degrees of freedom is t = +/- 2.093.
As the test statistic is not in critical region, the decision is fail to reject null hypothesis.
There is deficient evidence at 0.05 level of significance to refuse the claim that pi is 3.2.
It will be noted in the double speak, however it serves to exemplify the point. We would not dare to claim that pi was 3.2, even although this sample seems to exemplify this. The sample does not provide adequate evidence to show it is not 3.2; however there might be another sample somewhere that does give enough evidence. Therefore, we won't state it is 3.2; just that we do not have sufficient evidence to prove it is not 3.2.
Latest technology based Statistics Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Statistics help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Statistics, project ideas and tutorials. We provide email based Statistics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Statistics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Statistics Homework help and assignment help services. They use their experience, as they have solved thousands of the Statistics assignments, which may help you to solve your complex issues of Statistics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
Theory and lecture notes of class NP of problems solvable all along with the key concepts of the class np of problems solvable, Complexity P & NP, deterministic polynomial-time. Tutorsglobe offers homework help, assignment help and tutor’s assistance on class NP of problems solvable.
www.tutorsglobe.com offers system analysis to build a new system homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
tutorsglobe.com skin grafting assignment help-homework help by online skin tutors
tutorsglobe.com factors of production assignment help-homework help by online meaning of production tutors
tutorsglobe.com derivation of m-m equation assignment help-homework help by online enzyme kinetics tutors
Incompatibility mechanisms tutorial all along with the key concepts of Self-incompatibility in plants, Mechanisms of self-incompatibility, Gametophytic self-incompatibility, Heteromorphic self-incompatibility, Cryptic self-incompatibility, Self-compatibility
Theory and lecture notes of Resistive Configurations all along with the key concepts of resistors in series, kirchhoffs voltage law, resistors in parallel, potential divider and current splitting. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Resistive Configurations.
want to outshine among your classmates? come aboard with microeconomics assignment help at low prices and score high!
tutorsglobe.com iga and ige assignment help-homework help by online properties and functions of immunoglobulins tutors
tutorsglobe.com general characteristics assignment help-homework help by online spermatophytes tutors
Cost reduction programme aims at improvement of human efforts at all levels of the organisation which help in reducing costs.
Sound Section contains - MHz Trap Circuit, Sound IF Amplifier, Audio Amplifier, Speaker, regulated power supply.
tutorsglobe.com virus assignment help-homework help by online microbiology tutors
tutorsglobe.com paulings method assignment help-homework help by online calculation of atomic radius tutors
tutorsglobe.com debt securitization assignment help-homework help by online source of finance tutors
1959335
Questions Asked
3689
Tutors
1456206
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!