Using Mean and Mean Absolute Deviation to Compare Data - Quiz

The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed

algol [13]

Answer:

$\chi^2 = \frac{(27-33.33)^2}{33.33}+\frac{(31-33.33)^2}{33.33}+\frac{(42-33.33)^2}{33.33}+\frac{(40-33.33)^2}{33.33}+\frac{(28-33.33)^2}{33.33}+\frac{(32-33.33)^2}{33.33} =5.860$

$p_v = P(\chi^2_{5} >5.860)=0.32$

Since the p value is higher than the significance level assumed 0.05 we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we can assume that we have equally like results.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

Number: 1, 2 , 3 , 4 , 5 ,6

Frequency: 27, 31, 42, 40, 28, 32

We need to conduct a chi square test in order to check the following hypothesis:

H0: The outcomes are equally likely.

H1: The outcomes are not equally likely.

The level of significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The observed values are given:

$O_{1}=27$ $O_{2}=31$

$O_{3}=42$ $O_{4}=40$

$O_{5}=28$ $O_{6}=32$

The expected values are given by:

$E_{1} =\frac{1}{6}*200=33.33$ $E_{2} =\frac{1}{6}*200=33.33$

$E_{3} =\frac{1}{6}*200=33.33$ $E_{4} =\frac{1}{6}*200=33.33$

$E_{5} =\frac{1}{6}*200=33.33$ $E_{6} =\frac{1}{6}*200=33.33$

And now we can calculate the statistic:

$\chi^2 = \frac{(27-33.33)^2}{33.33}+\frac{(31-33.33)^2}{33.33}+\frac{(42-33.33)^2}{33.33}+\frac{(40-33.33)^2}{33.33}+\frac{(28-33.33)^2}{33.33}+\frac{(32-33.33)^2}{33.33} =5.860$

Now we can calculate the degrees of freedom for the statistic given by:

$df=Categories-1=6-1=5$

And we can calculate the p value given by:

$p_v = P(\chi^2_{5} >5.860)=0.32$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(5.860,5,TRUE)"

Since the p value is higher than the significance level assumed 0.05 we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we can assume that we have equally like results.

4 0

3 years ago

Can someone help me PLZ! I keep posting the same question and no ones helping me :((((((((((((

kipiarov [429]

Answer:

Multiply x + y = 3 by 3 and add it to -3x - 2y = -7

Step-by-step explanation:

When using elimination to solve a system of equations, you multiply one equation by some number. The reason for doing this is that when you add it to the second equation, you want one variable to cancel out. When one variable cancels out (in this case x), you can solve for the other variable (in this case y). I will show this:

3(x + y = 3) = 3x + 3y = 9

3x + 3y = 9

+ -3x + -2y = -7

---------------------------

y = 2

Now, knowing that y = 2, you can substitute y=2 into either equation to solve for x.

-3x - 2(2) = -7

-3x -4 = -7

-3x = -3

x = 1 | to double check (1, 2) as your answer plug these values into both equations

Finding this solution would not have been possible if not for cancelling out the x's above. The other three are wrong because none of the other options cancels out one of the variables.

3 0

3 years ago

Need help with math!!

fiasKO [112]

Answer:

1. Given

2. AAS

3. Reflexive

4. Definition of perpendicular

5. Definition of angle bisector

6. CPCTE

3 0

3 years ago

Which is bigger 600 km or 5 m

Lina20 [59]

600 km=600,000 m
So 600km is bigger than 5 m

7 0

3 years ago

Read 2 more answers

How far do US workers travel to get to their jobs? A researcher would like to collect information on the commute distance travel

Liono4ka [1.6K]

The first answer I have to just guess.

Step-by-step explanation:

4 0

1 year ago

Using Mean and Mean Absolute Deviation to Compare Data - Quiz - Level G