5

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

An urn contains six red balls and four green balls. A sample of seven balls is selected at random.

KIM [24]

There are 10 balls in the Urn Total.

Red: 6

Green: 4

Question One: The probability that five red and two green is selected is likely. (as that is over half for both)

Question Two: Impossible. There is only 6 red balls, and 7 are taken from the urn. Thus it would at most be possible for 6 red and 1 green.

Question Three: At least four is likely, as there is more red then green in the Urn.

Hope I helped!

(Mark Brainliest if you can please!)

5 0

3 years ago

Susan walks for 10 hours each week. Find the number of hours she walks in 1, 2, and 4 week(s).

natita [175]

She walks 70 hours in total 10 20 and 40

7 0

3 years ago

PLEASE HELP! A campground rents bicycles by the hour. The total cost y to rent a bicycle, including deposit, is presented by the

Lelu [443]

The domain and the range of the function are all possible values of the x and y, respectively, that function can take.
The range is given by:

$y_{o}= \frac{3}{3} +12 \\ y_{o}=12 \\ \\ y_{e}= \frac{27}{3} +12 \\ y_{e}=21 \\ \\ \boxed {Im=(y\in R \mid 12\leq y \leq 21)}$

The domain is given by:

$\boxed {D=(x\in R \mid 3\leq y \leq 27)}$

4 0

3 years ago

Determine the equation of the line passing through the points (3,1) and (5,−1).

katrin [286]

Answer:

y=-x+4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-1)/(5-3)

m=-2/2

m=-1

y-y1=m(x-x1)

y-1=-1(x-3)

y-1=-x+3

y=-x+3+1

y=-x+4

5 0

3 years ago