Which system of equations is represented by this graph?<br>y= _ x+3 <br>y=

The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

AURORKA [14]

The two nominal variables are related.

The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

Ownership C1 C2 C3

No 40 32 48

Yes 30 48 52

The first thing to do in order to determine if they are related or not is to state our null and alternative hypothesis

Null hypothesis

$\mathbf{H_o: Two \nomial \ variables \ are \ related}$

Alternative hypothesis

$\mathbf{H_a: Two \nomial \ variables \ are \ not \ related}$

Using the Chi-square test statistics which can be expressed by using the formula

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

Ownership C1 C2 C3 Total

No 40 32 48 120

Yes 30 48 52 130

Total 70 80 100 250

The expected values are calculated as:

$\mathsf{E_{a,b} = \dfrac{(row \ total \times column \ total )}{grand \ total }}$

$\mathsf{E_{1,1} = \dfrac{(70 \times120 )}{250 }}$

$\mathsf{E_{1,1} = 33.6}$

$\mathsf{E_{1,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{1,2} = 36.4}$

$\mathsf{E_{2,1} = \dfrac{(80 \times120 )}{250 }}$

$\mathsf{E_{2,1} = 38.4}$

$\mathsf{E_{2,2} = \dfrac{(80 \times 130 )}{250 }}$

$\mathsf{E_{2,2} = 41.6}$

$\mathsf{E_{3,1} = \dfrac{(100 \times120 )}{250 }}$

$\mathsf{E_{3,1} = 48}$

$\mathsf{E_{3,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{3,2} = 52}$

∴ Using the Chi-square test statistics, we have:

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

$X ^2 = \Bigg( \dfrac{(40-33.6)^2}{33.6}+ \dfrac{(30-36.4)^2}{36.4}+ \dfrac{(32-38.4)^2}{38.4}+ \dfrac{(48-41.6)^2}{41.6} + \dfrac{(48-48)^2}{48}+ \dfrac{(52-52)^2}{52} \Bigg)$

$X ^2 = \Bigg( \dfrac{40.96}{33.6}+ \dfrac{40.96}{36.4}+ \dfrac{40.96}{38.4}+ \dfrac{40.96}{41.6} + \dfrac{0}{48}+ \dfrac{0}{52} \Bigg)$

$X ^2 = \Bigg( 1.2190+ 1.1253+ 1.0667+ 0.9846+0+ 0 \Bigg)$

$\mathbf{X ^2 =4.3956}$

The degree of freedom df = ((r - 1) × (c - 1))

= (3 - 1) (2 -1 )

= 2 × 1

= 2

∴

Assuming the level of significance = 5%

The p-value of the Chi-square test statistics at df of 2 is:

= $\mathbf{P(X^2 > 4.3956) \implies 0.111}$

Therefore, we can conclude that since the p-value (0.111) is greater than the level of significance (0.05), we fail to reject the null hypothesis.

Hence, the two nominal variables are related.

Learn more about Chi-square test statistics here:

brainly.com/question/2365682?referrer=searchResults

7 0

3 years ago

John is x years old and his sister Mary is (5x-12) years old. Given that Mary is twice as old as John, write in terms of x an eq

jeka57 [31]

Answer: x =4
Mary is 8 and John is 4

Explanation:
John = x
Mary = 5x - 12 or 2x

Solve for x

5x - 12 = 2x

-12 = -3x

X=4

Hope that helps!

3 0

3 years ago

Express the negations of each of these statements so that all negation symbols immediately precede predicates. a. ∃z∀y∀xT (x, y,

Bess [88]

Answer:

As shown in the attachment

Step-by-step explanation:

The application of De Morgan's Law was applied as shown in the attachment.

3 0

4 years ago

(30 POINTS!!!) Suppose △ABC≅△LMN .

Mandarinka [93]

The correct answer would be the first and the last ones.

5 0

3 years ago

Read 2 more answers

Danielle wants to paint her daughter's room pink. Which plan will give her paint that is the least red?

NeTakaya

Step-by-step explanation:

Plan B:

2:5 = 0.4 red to 1 white

1:4 = 0.25 red to 1 white

Students might also scale up using part-to-whole-ratios and come up with 35 parts total and 14 parts red for Plan A and 35 parts total and 7 parts red for Plan B.

8 0

3 years ago

Which system of equations is represented by this graph?y= _ x+3 y= _ x-3​

Which system of equations is represented by this graph?y= _ x+3 y= _ x-3