Mathematics, 24.04.2020 02:53 Petlover6975

Two 95 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and J. One confidence interval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J.

When all other things remain the same, which of the following describes the relationship between the two confidence intervals?

a)The width of i400 will be 4 times the width of i100.
b) The width of i400 will be 2 times the width of i100
c)The width of i400 will be equal to the width of i100.
d)The width of I400 will be 1/2 times the width of I100
e)The width of I400 will be 1/4 times the width of I100.

Answers: 1

Show answers

Answers

Answer from: Victoriag2626

e)The width of I400 will be 1/4 times the width of I100.

Step-by-step explanation:

If the confidence interval is 95% = 0.95, therefore α = 1 - 0.95 = 0.05.

$\frac{\alpha }{2} =\frac{0.05}{2}=0.0025$

The width of the confidence (W) is given by the equation:

$W=\frac{z_{\frac{\alpha }{2} }*\sigma}{\sqrt{n} }$ , where n is the sample size, $\sigma$ is the standard deviation and $z_{\frac{\alpha }{2} }$ is the z score of α/2

From the equation, we can see that the width is inversely proportional to the square root of the sample size.

Since nterval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J. and all other things remain the same.

Let $W_{I4$ be the width of I400 and $W_{I1$ be the width of I100. Therefore:

$W_{I4}=\frac{z_{\frac{\alpha }{2} }*\sigma}{\sqrt{400} }=\frac{z_{\frac{\alpha }{2} }*\sigma}{4 }\\And, W_{I1}=\frac{z_{\frac{\alpha }{2} }*\sigma}{\sqrt{100} }=\frac{z_{\frac{\alpha }{2} }*\sigma}{1 }\\Therefore,\frac{W_{I4}}{W_{I1}} =\frac{\frac{z_{\frac{\alpha }{2} }*\sigma}{4 }}{\frac{z_{\frac{\alpha }{2} }*\sigma}{1 }}\\\frac{W_{I4}}{W_{I1}}=\frac{1}{4}\\ W_{I4}=\frac{1}{4}W_{I1}$

The width of I400 will be 1/4 times the width of I100.

Answer from: Quest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Answer from: Quest

P(chicago, illinois)

Another question on Mathematics

Mathematics, 21.06.2019 16:30

Adam plans to choose a video game from the section of the store where everything is 75% off. he writes the expression d-0.75d to find the sale price of the game if the original price is d dollars. gena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars. use the drop down menus to explain each part of adams and rena's expression

Answers: 3

Answer

Mathematics, 21.06.2019 18:00

Me asap! what is the slope of this line? enter your answer in the box.

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

For f(x) = 3x+1 and g(x) = x2 - 6, find (g/f)(x)

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Which of the following graphs could represent a cubic function?