All categories

3 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Mathematics

1 answer:

Archy [21]3 years ago

5 0

Answer:

The standard deviation of the difference is 4.53

Step-by-step explanation:

Here we have the formula for the combined estimate of the variance given as

$S^2_c = \frac{S^2_1(n_1-1)+S^2_2(n_1-1)}{(n_1-1)+(n_2-1)}$

Where:

S $_c$ ² = Combined variance

n₁ = Sample size of the sample of boys = 8

n₂ = Sample size of the sample of girls = 8

S₁² = Variance of the first sample of boys = 10²

S₂² = Variance of the second sample of girls = 8²

Therefore we have

$S^2_c = \frac{10^2(8-1)+8^2(8-1)}{(8-1)+(8-1)}$

S $_c$ ² = 82

The variance of the difference between the two mean is;

$S^2_{(\bar {x}_1-\bar {x}_1)} = \frac{S^2_c}{n_1}+\frac{S^2_c}{n_2} =2\times \frac{82}{8}$ = 20.5

Therefore the standard deviation of the difference is √20.5 = 4.53.

You might be interested in

AB is a straight line workout the size of angle X

Hoochie [10]

The x value will be 109°. The straight line formed a 180° angle. Solving the equation yields the angle.

<h3>What are supplementary angles?</h3>

Supplementary angles are two angels whose sum is 180°. When a straight line intersects a line, two angles form on each of the sides of the considered straight line.

Those two-two angles are supplementary angles in two pairs. That is, if two supplementary angles are adjacent to each other, their exterior sides form a straight line.

The straight line formed a 180° angle. The resulting equation is as follows:

⇒x+42°+29°=180°

⇒x=109°

Hence, the value of the x will be 109°

The complete question is:

AB is a straight line.

Work out the size of angle x.

Not drawn accurately

42°

29°

To learn more about supplementary angles, refer to:

brainly.com/question/12919120

#SPJ1

4 0

1 year ago

Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is partic

o-na [289]

Answer:

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

b) $n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

Part b

For thi case the estimator for p is $\hat p =0.07$

$n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

4 0

3 years ago

Stan wants to start an IRA that will have $250,000 in it when he retires in 25 years. How much should he invest semiannually in

Alecsey [184]

$1,041,666.70 I'm not sure but that what I think the answer is

8 0

3 years ago

The point slope form of the equation of the line that passes through (-5,-1) and (10,-7) is y+7= -2/5(x-10) what is the standard

Alex787 [66]

Standard form for y+7=-2/5(x-10) is y=-7-2/5(x-10)

3 0

3 years ago

The table below shows the transportation method of all of the employees who work at the mall. What percent of employees walk to

Pepsi [2]

Answer:

0.005 or 0.5% walk

Step-by-step explanation:

Total:

758 + 530 + 7 + 105 = 1400

To find how many employees walk:

7/1400 = 0.005

6 0

3 years ago