Can someone help please

Let n1equals50, Upper X 1equals30, n2equals50, and Upper X 2equals10. Complete parts (a) and (b) below. a. At the 0.05 leve

Viefleur [7K]

Answer:

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

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

$z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082$

$p_v =2*P(Z>4.082)=4.46x10^{-5}$

So the p value is a very low value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.

Step-by-step explanation:

1) Data given and notation

$X_{1}=30$ represent the number of people with a characteristic in 1

$X_{2}=10$ represent the number of people with a characteristic in 2

$n_{1}=50$ sample of 1 selected

$n_{2}=50$ sample of 2 selected

$p_{1}=\frac{30}{50}=0.6$ represent the proportion of people with a characteristic in 1

$p_{2}=\frac{10}{50}=0.2$ represent the proportion of people with a characteristic in 2

z would represent the statistic (variable of interest)

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

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion 1 is different from proportion 2 , 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)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{30+10}{50+50}=0.4$

3) Calculate the statistic

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

$z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082$

4) Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a two sided test the p value would be:

$p_v =2*P(Z>4.082)=4.46x10^{-5}$

So the p value is a very low value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.

3 0

3 years ago

A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received wit

m_a_m_a [10]

Answer:

The probability that the message will be wrong when decoded is 0.05792

Step-by-step explanation:

Consider the provided information.

To reduce the chance or error, we transmit 00000 instead of 0 and 11111 instead of 1.

We have 5 bits, message will be corrupt if at least 3 bits are incorrect for the same block.

The digit transmitted is incorrectly received with probability p = 0.2

The probability of receiving a digit correctly is q = 1 - 0.2 = 0.8

We want the probability that the message will be wrong when decoded.

This can be written as:

$P(X\geq3) =P(X=3)+P(X=4)+P(X=5)\\P(X\geq3) =\frac{5!}{3!2!}(0.2)^3(0.8)^{2}+\frac{5!}{4!1!}(0.2)^4(0.8)^{1}+\frac{5!}{5!}(0.2)^5(0.8)^0\\P(X\geq3) =0.05792$

Hence, the probability that the message will be wrong when decoded is 0.05792

4 0

2 years ago

what is the equation in slope intercept form of the line that passes through the point (-4,47) and (2,-16)

Vilka [71]

The slope-intercept form:

$y=mx+b$

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-4, 47) and (2, -16). Substitute:

$m=\dfrac{-16-47}{2-(-4)}=\dfrac{-63}{6}=-\dfrac{63:3}{6:3}=-\dfrac{21}{2}$

Therefore we have:

$y=-\dfrac{21}{2}x+b$

Put the coordinates of the point (2, -16) to the equation:

$-16=-\dfrac{21}{2}(2)+b\\\\-16=-21+b\qquad\text{add 21 from both sides}\\\\5=b\to b=5$

Answer: $\boxed{y=-\dfrac{21}{2}x+5}$

6 0

3 years ago

Arrange from least to greatest 3,-3, 1, -5, 0, -2, -1, 4, 6.

Darina [25.2K]

Answer:

Step-by-step explanation:

-5,-3,-2,-1,0,1,3,4,6

8 0

3 years ago

Two airplanes leave an airport at the same time. One airplane travels at 400 km/h

Neko [114]

Answer:

912.414

Step-by-step explanation:

The angle

θ

between the directions of motion of planes

θ

=

320

−

200

=

120

∘

The distance

a

traveled by first plane flying at a speed of

150

km/hr

in

3

hrs

a

=

150

⋅

3

=

450

k

m

Similarly, the distance

b

traveled by second plane flying at a speed of

200

km/hr

in

3

hrs

b=

200x3=

600 km

Now, the distance between the planes after 3

hrs will be equal to the side of a triangle opposite to the angle θ=120∘

included by the sides

a

=

450

& b=

600

.

Now, using Cosine rule in the concerned triangle, the distance between the plane after

3

hours is given as

4 0

2 years ago