Help ASAP with these questions.

A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95% confidence interval will be c

Anna [14]

Answer:

The interval from the sample of size 400 will be approximately <u>One -half as wide</u> as the interval from the sample of size 100

Step-by-step explanation:

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the 95% confidence interval is dependent on the value of the margin of error at a constant sample mean or sample proportion

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

Here assume that $Z_{\frac{\alpha }{2} } \ and \ \sigma \$ is constant so

$E = \frac{k}{\sqrt{n} }$

=> $E \sqrt{n} = K$

=> $E_1 \sqrt{n}_1 = E_2 \sqrt{n}_2$

So let $n_1 = 400$ and $n_2 = 100$

=> $E_1 \sqrt{400} = E_2 \sqrt{100}$

=> $E_1 = \frac{\sqrt{100} }{\sqrt{400} } E_2$

=> $E_1 = \frac{1}{2 } E_2$

So From this we see that the confidence interval for a sample size of 400 will be half that with a sample size of 100

7 0

2 years ago

Find the equation of the straight line passing through the point (0,1) which is perpendicular to the line y= -2x + 2

mylen [45]

Answer:

y = 1/2x + 1

In order to evaluate a slope that is perpendicular to the given equation, you need to find the opposite reciprocal of the original slope. This means you take the original slope, flip the numerator and the denominator, and change the sign in front.

-2 ⇒ 1/2

Next, we need to substitute the information given into the point-slope formula.

The point-slope formula is:

y - y₁ = m(x - x₁)

y - 1 = 1/2(x - 0)

y - 1 = 1/2x

y = 1/2x + 1

Therefore, the line perpendicular to y = -2x + 2 is y = 1/2x + 1.

6 0

3 years ago

A scale model of a rectangular building lot measures 7feet by 5 feet. If the actual house will be built using a scale factor of

Tamiku [17]

Actual area of the rectangular building = 5040 feet²
Step-by-step explanation:
Length of the rectangular building = 7 feet
Width of the rectangular building = 5 feet
Now, The building is made with a scale factor of 12
So, Actual length of the rectangular building = 84 feet
Actual width of the rectangular building = 60 feet
Now, Actual area of the rectangular building = Length × Width
⇒ Actual area of the rectangular building = 84 × 60
⇒ Actual area of the rectangular building = 5040 feet²

5 0

2 years ago

The top option, "meat lovers", received 12 votes. Was this majority of the votes?

ICE Princess25 [194]

Answer:

Step-by-step explanation:

if the number of votes is 25, 12 is not majority

but if the number is 23 then 12 is majority

6 0

3 years ago

Two trains, Train A and Train B, weigh a total of 493 tons. Train A is heavier than Train B. The difference of their weights is

Vladimir79 [104]

Answer: Area of the floor or ceiling: Multiply the length by the width (10 feet x 12 ... feet (10 feet wide x 8 feet high) and the other is 96 square feet (12 feet x 8 feet). ... divide the total square footage of the floor by 9 (120 square feet / 9 ... To convert an area from square feet into square inches, simply multiply by 144.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers