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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 One -half as wide 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

20 points five stars a thank you, dont need to awnser first. i will repeat this question every 3 and a half minutes. ive got nin

melomori [17]

Answer:

Thanks, you are so generous

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

. Complete the missing steps in the paragraph proof of Theorem 3-8.

Crank

To solve for the missing steps, let's rewrite first the problem.

Given:

In a plane, line m is perpendicular to line t or m⟂t
line n is perpendicular to line t or n⟂t

Required:

Prove that line m and n are parallel lines

Solution:

We know that line t is the transversal of the lines m and n.

With reference to the figure above,

∠ 2 and ∠ 6 are right angles by definition of perpendicular lines. This states that if two lines are perpendicular with each other, they intersect at right angles.

So ∠ 2 ≅ ∠ 6. Since corresponding angles are congruent.

Therefore, line m and line n are parallel lines.

ANSWERS: perpendicular lines, corresponding

8 0

3 years ago

the width of a rectangle is 5 meters less than it’s length. The area of the rectangle is 84m^2. Find the length and width of the

larisa [96]

16.8m is the length and 5m is width

3 0

3 years ago

HELP ME PLSSS OMG OMG PLS THIS IS A BIG LART OF MY GRADE ON A TWST AND I RLLY RLLY NEED IT PLE HELP

Elza [17]

Answer: The answer is B.

6 0

2 years ago

Read 2 more answers