|2x + 5| = 13 please show work

A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second po

igor_vitrenko [27]

Answer:

a) For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b) Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c) $z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

Step-by-step explanation:

Data given and notation

$X_{1}=170$ represent the number of people with the characteristic 1

$X_{2}=110$ represent the number of people with the characteristic 2

$n_{1}=200$ sample 1 selected

$n_{2}=150$ sample 2 selected

$p_{1}=\frac{170}{200}=0.85$ represent the proportion estimated for the sample 1

$p_{2}=\frac{110}{150}=0.733$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

a.State the decision rule.

For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b. Compute the pooled proportion.

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c. Compute the value of the test statistic.

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d. What is your decision regarding the null hypothesis?

Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

5 0

3 years ago

2.386 rounded to the nearest tenth

svetoff [14.1K]

Answer:

Los números decimales son una combinación de números enteros y números que se encuentran entre los números enteros. A veces es importante poder comparar decimales para saber cuál es mayor. Por ejemplo, si alguien corrió los 100 metros planos en 10.57 segundos, y alguien más los corrió en 10.67 segundos, puedes comparar los decimales para determinar qué tiempo es más rápido. Saber cómo comparar decimales requiere el entendimiento del valor de posición decimal, y es similar a comprar números enteros.

Cuando trabajamos con decimales, hay veces que no se necesita un número preciso. En tal caso, es útil redondear números decimales. Por ejemplo, si la bomba de una gasolinera muestra que llenaste el tanque del carro de un amigo con 16.478 galones de gasolina, podrías querer redondear el número y decirle a tu amigo que le pusiste 16.5 galones.

Step-by-step explanation:

Otra forma de comparar decimales es comparar los dígitos en cada número, empezando con el lugar de posición mayor, que es el de la izquierda. Cuando un dígito en un número decimal es mayor que el dígito correspondiente en el otro número, entonces ése número decimal es mayor.

Por ejemplo, primero compara los dígitos de las décimas. Si son iguales, continúa con el lugar de las centésimas. Si esos dígitos no son iguales, el decimal con el dígito mayor es el número decimal mayor. Observa cómo se hace esto en los ejemplos siguientes.

6 0

3 years ago

How many equivalence relations are there on the set 1, 2, 3]?

Alex787 [66]

Answer:

We need to find how many number of equivalence relations are on the set {1,2,3}

A relation is an equivalence relation if it is reflexive, transitive and symmetric.

equivalence relation R on {1,2,3}

1.For reflexive, it must contain (1,1),(2,2),(3,3)

2.For transitive, it must satisfy: if (x,y)∈R then (y,x)∈R

3. For symmetric, it must satisfy: if (x,y)∈R,(y,z)∈R then (x,z)∈R

Since (1,1),(2,2),(3,3) must be there is R, (1,2),(2,1),(2,3),(3,2),(1,3),(3,1). By symmetry,

we just need to count the number of ways in which we can use the pairs (1,2),(2,3),(1,3) to construct equivalence relations.

This is because if (1,2) is in the relation then (2,1) must be there in the relation.

the relation will be an equivalence relation if we use none of these pairs (1,2),(2,3),(1,3) . There is only one such relation: {(1,1),(2,2),(3,3)}

we can have three possible equivalence relations:

{(1,1),(2,2),(3,3),(1,2),(2,1)}

{(1,1),(2,2),(3,3),(1,3),(3,1)}

{(1,1),(2,2),(3,3),(2,3),(3,2)}

6 0

3 years ago

Select all that apply. the theorems in the lesson are followed by which of the following?

musickatia [10]

Answer: E

Step-by-step explanation: In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. ... Many mathematical theorems are conditional statements.

7 0

3 years ago

Read 2 more answers

Which expression represents the area of the garden in square feet?

Kisachek [45]

Answer:

C. 42x² - 3x - 9

Step-by-step explanation:

Area:

(7x + 3) (6x - 3)

7x(6x - 3) + 3(6x - 3)

42x² - 21x + 18x - 9

42x² - 3x - 9

8 0

3 years ago