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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

You need to haul a load of patio bricks to a job site. Each brick weighs 4 pounds 14 ounces. Truck can carry a 3/4 - ton load. H

Olin [163]

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

6 0

3 years ago

NEED HELP FAST PLEASE Evaluate the limit. a.4 c.1 b.2 d.limit does not exist

BlackZzzverrR [31]

We have the following limit:
(8n2 + 5n + 2) / (3 + 2n)
Evaluating for n = inf we have:
(8 (inf) 2 + 5 (inf) + 2) / (3 + 2 (inf))
(inf) / (inf)
We observe that we have an indetermination, which we must resolve.
Applying L'hopital we have:
(8n2 + 5n + 2) '/ (3 + 2n)'
(16n + 5) / (2)
Evaluating again for n = inf:
(16 (inf) + 5) / (2) = inf
Therefore, the limit tends to infinity.
Answer:
d.limit does not exist

7 0

3 years ago

Making Connections Read the word problem. Use the review vocabulary to describe what each number represents.

Wittaler [7]

Answer:

dividend, divisor, quotient

Step-by-step explanation:

The answers are in the same order as the vocabulary words

8 0

2 years ago

For an activity in class, students used pieces of string to measure roads on a map. They used a map scale to determine the dista

jeka57 [31]

Answer:

C 152

Step-by-step explanation:

Beacuse it is. Hope that helps

4 0

3 years ago

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