Write an equation of a line that is parallel to the line y = 2x + 8

Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing i

Nina [5.8K]

Answer:

$z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358$

$p_v =2*P(Z>5.358) = 4.2x10^{-8}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.

Step-by-step explanation:

Data given and notation

$X_{1}=253$ represent the number with no defects in sample 1

$X_{2}=196$ represent the number with no defects in sample 1

$n_{1}=300$ sample 1

$n_{2}=300$ sample 2

$p_{1}=\frac{253}{300}=0.843$ represent the proportion of number with no defects in sample 1

$p_{2}=\frac{196}{300}=0.653$ represent the proportion of number with no defects in sample 2

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 in the the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

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 $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{253+196}{300+300}=0.748$

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.

Calculate the statistic

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

$z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358$

Statistical decision

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

$p_v =2*P(Z>5.358) = 4.2x10^{-8}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.

5 0

3 years ago

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Cloud [144]

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7 0

3 years ago

Read 2 more answers

Fill in the blanks below.

Dmitry_Shevchenko [17]

Answer:

a) Slope of the line m = ∞

b) Slope of the line m =0

Step-by-step explanation:

Explanation:-

Step(i):-

Given points are ( 7,7) and (7,-8)

Slope of the line

$m = \frac{y_{2} - y_{1} }{x_{2}-x_{1} }$

$m = \frac{-8-7 }{7-7 } = \frac{-15}{0} = infinite$

m = ∞

Step(ii):-

Given points are (-6,7) and (9,7)

Slope of the line

$m = \frac{y_{2} - y_{1} }{x_{2}-x_{1} }$

$m = \frac{7-7 }{9-(-6) } = \frac{0}{15} = 0$

Slope of the line m =0

6 0

3 years ago

I don't know how to do this problem.....please help

Lemur [1.5K]

I hope this helps you

5 0

3 years ago

The altitude of a plane is 1200 meters. From a point on the ground, the angle of elevation of an airplane is 25º. What is the di

gtnhenbr [62]

Answer:

2839.4 meters

Step-by-step explanation:

Given that:

Altitude = 1200 m

Using trigonometry :

The distance from point P to the airplane :

Using trigonometric relation :

Sin θ = opposite / hypotenus

Sin θ = altitude / x

Sin θ = 1200 m / x

Sin 25 = 1200 / x

0.4226182 = 1200 / x

x = 1200 / 0.4226182

x = 2839.4423

Distance from P to airplane = 2839.4 meters

8 0

3 years ago

Write an equation of a line that is parallel to the line y = 2x + 8￼

Write an equation of a line that is parallel to the line y = 2x + 8