I have 100 boxes and on each of them there is a button. When you press the button, a random number appears on a screen on the box.In 99 of the 100 boxes, the random number is chosen from a normal distributionwith expected value μ1 = 7 and standard deviation σ1 = 3. We call these boxesModel 1. In the last box, the random number is selected from a normal distributionwith expected value μ2 = 8 and standard deviation σ2 = 2. We call these boxesModel 2.A random box is selected and I press the button a few times before claimingthat this is a Model 1 box. You're not sure if you should trust me, andwould like to inspect the box yourself.(a) Formulate a hypothesis test where the null hypothesis is that this is a Model1 box. What kind of hypothesis test (normal distribution, t-distribution, χ2 distribution)Do you use and why? What do you choose as the significance level and why? IsIs this a one-sided or two-sided hypothesis test? Whether one-sided, right-sided orleft sided?(b) If you can press the box's button 10 times, what must be the sum of valuesbe for you to reject the null hypothesis?(c) You press the button 10 times, and get that the sum of the values is 102.Before you can reject the null hypothesis, I claim that this sum orhigher is actually more likely if it is a Model 1 box than ifit is a Model 2 box. Explain why this might be true. Rain lookedthe probabilities of getting a sum of 102 or higher for both a Model1 box and a Model 2 box.(d) Explain what it is about this situation that makes the hypothesis test wrongto use if the sum becomes very high. .Jeg har 100 bokser, og på hver av dem er det en knapp. Når du trykker påknappen, vises et tilfeldig tall på en skjerm på boksen.I 99 av de 100 boksene velges det tilfeldige tallet fra en normalfordelingmed forventningsverdi #₁ = 7 og standardavvik 0₁ 3. Vi kaller disse bokseneModell 1. I den siste boksen velges det tilfeldige tallet fra en normalfordelingmed forventningsverdi 2 = 8 og standardavvik 0₂ = 2. Vi kaller disse bokseneModell 2.En tilfeldig boks velges, og jeg trykker på knappen noen ganger, før jeg påstårat dette er en Modell 1-boks. Du er ikke sikker på om du burde stole på meg, ogønsker å selv inspisere boksen.(a) Formuler en hypotesetest hvor nullhypotesen er at dette er en Modell1-boks. Hva slags hypotesetest (normalfordeling, t-fordeling, x²-fordeling)bruker du og hvorfor? Hva velger du som signifikansnivå og hvorfor? Erdette en ensidig eller tosidig hypotesetest? Om ensidig, høyresidig ellervenstresidig?(b) Om du får trykke på boksens knapp 10 ganger, hva må summen av verdiervære for at du skal forkaste nullhypotesen?(c) Du trykker på knappen 10 ganger, og får at summen av verdiene er 102.Før du rekker forkaste nullhypotesen, påstår jeg at denne summen ellerhøyere faktisk er mer sannsynlig om det er en Modell 1-boks enn omdet er en Modell 2-boks. Forklar hvorfor dette kan stemme. Regn så utsannsynlighetene for å få en sum på 102 eller høyere for både en Modell1-boks og en Modell 2-boks.(d) Forklar hva det er med denne situasjonen som gjør at hypotesetest blir feilå bruke dersom summen blir veldig høy.

(a) The hypothesis test to determine if the box is a Model 1 box can be formulated as follows: Null…

I have 100 boxes and on each of them there is a button. When you press the button, a random number appears on a screen on the box. In 99 of the 100 boxes, the random number is chosen from a normal distribution with expected value μ1 = 7 and standard deviation σ1 = 3. We call these boxes Model 1. In the last box, the random number is selected from a normal distribution with expected value μ2 = 8 and standard deviation σ2 = 2. We call these boxes Model 2. A random box is selected and I press the button a few times before claiming that this is a Model 1 box. You're not sure if you should trust me, and would like to inspect the box yourself. (a) Formulate a hypothesis test where the null hypothesis is that this is a Model 1 box. What kind of hypothesis test (normal distribution, t-distribution, χ2 distribution) Do you use and why? What do you choose as the significance level and why? Is Is this a one-sided or two-sided hypothesis test? Whether one-sided, right-sided or left sided? (b) If you can press the box's button 10 times, what must be the sum of values be for you to reject the null hypothesis? (c) You press the button 10 times, and get that the sum of the values is 102. Before you can reject the null hypothesis, I claim that this sum or higher is actually more likely if it is a Model 1 box than if it is a Model 2 box. Explain why this might be true. Rain looked the probabilities of getting a sum of 102 or higher for both a Model 1 box and a Model 2 box. (d) Explain what it is about this situation that makes the hypothesis test wrong to use if the sum becomes very high.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

I have 100 boxes and on each of them there is a button. When you press the button, a random number appears on a screen on the box.
In 99 of the 100 boxes, the random number is chosen from a normal distribution
with expected value μ1 = 7 and standard deviation σ1 = 3. We call these boxes
Model 1. In the last box, the random number is selected from a normal distribution
with expected value μ2 = 8 and standard deviation σ2 = 2. We call these boxes
Model 2.
A random box is selected and I press the button a few times before claiming
that this is a Model 1 box. You're not sure if you should trust me, and
would like to inspect the box yourself.
(a) Formulate a hypothesis test where the null hypothesis is that this is a Model
1 box. What kind of hypothesis test (normal distribution, t-distribution, χ2 distribution)
Do you use and why? What do you choose as the significance level and why? Is
Is this a one-sided or two-sided hypothesis test? Whether one-sided, right-sided or
left sided?
(b) If you can press the box's button 10 times, what must be the sum of values
be for you to reject the null hypothesis?
(c) You press the button 10 times, and get that the sum of the values is 102.
Before you can reject the null hypothesis, I claim that this sum or
higher is actually more likely if it is a Model 1 box than if
it is a Model 2 box. Explain why this might be true. Rain looked
the probabilities of getting a sum of 102 or higher for both a Model
1 box and a Model 2 box.
(d) Explain what it is about this situation that makes the hypothesis test wrong
to use if the sum becomes very high.

.
Jeg har 100 bokser, og på hver av dem er det en knapp. Når du trykker på
knappen, vises et tilfeldig tall på en skjerm på boksen.
I 99 av de 100 boksene velges det tilfeldige tallet fra en normalfordeling
med forventningsverdi #₁ = 7 og standardavvik 0₁ 3. Vi kaller disse boksene
Modell 1. I den siste boksen velges det tilfeldige tallet fra en normalfordeling
med forventningsverdi 2 = 8 og standardavvik 0₂ = 2. Vi kaller disse boksene
Modell 2.
En tilfeldig boks velges, og jeg trykker på knappen noen ganger, før jeg påstår
at dette er en Modell 1-boks. Du er ikke sikker på om du burde stole på meg, og
ønsker å selv inspisere boksen.
(a) Formuler en hypotesetest hvor nullhypotesen er at dette er en Modell
1-boks. Hva slags hypotesetest (normalfordeling, t-fordeling, x²-fordeling)
bruker du og hvorfor? Hva velger du som signifikansnivå og hvorfor? Er
dette en ensidig eller tosidig hypotesetest? Om ensidig, høyresidig eller
venstresidig?
(b) Om du får trykke på boksens knapp 10 ganger, hva må summen av verdier
være for at du skal forkaste nullhypotesen?
(c) Du trykker på knappen 10 ganger, og får at summen av verdiene er 102.
Før du rekker forkaste nullhypotesen, påstår jeg at denne summen eller
høyere faktisk er mer sannsynlig om det er en Modell 1-boks enn om
det er en Modell 2-boks. Forklar hvorfor dette kan stemme. Regn så ut
sannsynlighetene for å få en sum på 102 eller høyere for både en Modell
1-boks og en Modell 2-boks.
(d) Forklar hva det er med denne situasjonen som gjør at hypotesetest blir feil
å bruke dersom summen blir veldig høy.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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