A circle with a radius of 10,20 or 4 inches has a central angle of 0.25 radians that intercepts an arc of 25,5 or 16 inches

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

Hannah can paint a room in 8 hours. Destiny can paint the same room in 6 hours. How long does it take for both Hannah and Destin

Ksivusya [100]

Answer:

3 hours 26 minutes

Step-by-step explanation:

1/8 + 1/6 = 1/t where t is the required time in hours.

Multiply through by 24t:-

3t + 4t = 24

7t = 24

t = 3 3/7 hours

or 3 hours 26 minutes to the nearest minute.

6 0

3 years ago

One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 510,

Brums [2.3K]

Answer:

82

Step-by-step explanation:

solve a + (3a) + (a + 100)=510

7 0

3 years ago

fladli sells televisions. He earns a fixed amount for each television and an additional $ 20 if the buyer gets an extended warra

ivanzaharov [21]

Answer: $80

Step-by-step explanation:

Given: The amount earned by Fadil on selling 14 televisions= $1400

Therefore, the amount he earned on selling 1 television= $\frac{1400}{14}=\$100$

Since, he sold televisions with extended warranty and he earns $20 additional for it.

Then, the fixed amount Fadil earns for each television= $\$100-\$20=\$80$

Hence, Fadil earns $80 as the fixed amount for each televison.

4 0

3 years ago

A manufacturer of lawnmowers wanted to know the most important product attributes to consumers. The company's research team deve

stepladder [879]

Answer: Ordinal measurement scale

Step-by-step explanation:

In ordinal measurement scale the order of values or variables are very important. Just as in the case above, the rating from 1-3 is according to the order of it's importance.

Thanks

7 0

2 years ago