У = 2х – 6<br>у = х2

Answer:

The null hypothesis is $H_0: p \geq 0.2$

The alternative hypothesis is $H_1: p < 0.2$

The p-value of the test is of 0.0154 > 0.01, which means that at the 0.01 significance level, there is not significant evidence that the return rate is less than 20%.

Step-by-step explanation:

Test the claim that the return rate is less than 20%.

At the null hypothesis, we test if the return rate is of at least 20%, that is:

$H_0: p \geq 0.2$

At the alternative hypothesis, we test if the return rate is less than 20%, that is:

$H_1: p < 0.2$

Normal distribution as an approximation to the binomial distribution to find the Z-score.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

0.2 is tested at the null hypothesis. Sample of 6957.

This means that $p = 0.2, n = 6957$ . So

$\mu = E(X) = np = 6957*0.2 = 1391.4$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6957*0.2*0.8} = 33.36$

1319 surveys returned

This means that, due to continuity correction, $X = 1319 + 0.5 = 1319.5$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1319.5 - 1391.4}{33.36}$

$Z = -2.16$

P-value of the test:

The p-value of the test is the probability of 1319 or less people returning the survey, which is the p-value of Z = -2.16.

Looking at the z-table, Z = -2.16 has a p-value of 0.0154.

The p-value of the test is of 0.0154 > 0.01, which means that at the 0.01 significance level, there is not significant evidence that the return rate is less than 20%.

7 0

3 years ago

What is the product of a+3 and −2a2+15a+6b2?

Lady bird [3.3K]

Answer:

c. 2a3+9a2+45a+6ab2+18b2

Step-by-step explanation:

(a+3) + (−2a2+15a+6b2)

Using distributed p. with and a and 3

a(−2a2) + a(15a) +a(6b2) and 3(−2a2) + 3(15a) + 3(6b2)

= -−2a3 + 15a2 + 6ab2 = -6a2 + 45a + 18b2

Now add like terms and put in standard form.

15a2+(-6a2) = 9a2

And equals

-2a3 + 9a2+45a+6ab2+18b2

Trust me I took the test and got 100%

Your welcome,

7 0

3 years ago

Read 2 more answers

Hi I have these couple of questions here I'm really confused and I've been working on all of these for about three days now but

m_a_m_a [10]

Answer:

First Image:

1. 3/10

2. 9/10

3. 10

4. -5/3

5. 2/5

6. -5/2

Second Image:

10. y=x-2

Third Image:

1. y=-4/3x-3

2. y=4x-4

3. y=-3/4x+4

4. y=1/3x+3

Step-by-step explanation:

When graphing linear lines, there are just a few, simple things to look out for. The first thing is to look at how far the line goes until it goes through a second point. The second thing is to look at where the line crosses on the y-axis (the vertical barrier). When writing an equation for a linear line, the standard form is y=mx+b, where m is a placeholder for the slope of the line and b is the placeholder for the y-intercept (where the line crosses the y-axis). If the line goes from the upper left to the lower right, the slope is negative. On the other hand, if the line goes from the lower left to the upper right, the slope is positive. When deciding what the slope is, remember that it is written as Rise/Run. So, for example, the second problem in the first image shows a line that goes from the lower left to the upper right, meaning that the slope will be positive. Now, if you look at the red dot at the bottom of the line, just count each box upwards, until you are level with the other red dot at the top right of the graph. Once you have gotten your number (it should be nine), just count the boxes going to the right of where you ended, all the way until you reach the red dot at the top right (you should have counted 10). Now that you have those two numbers, you are able to plug them into Rise/Run. Since you went up nine blocks and right ten blocks, you would write the slope as 9/10. The slope is positive, therefore there is no sign in front of the slope. However, if the slope was negative, then you'd write it as -9/10. Now that you have the slope, you can plug it into the equation. The equation should now look like this: y=9/10x+b. Lastly, you must find the y-intercept. In order to do this, just simply look at the y-axis (the bolded, center line) to see where the line crosses. You should see that it crosses at the halfway point between one and zero, meaning the y-intercept is 1/2, or 0.5. With this, once again plug the value into the equation, which should now look like this: y=9/10x+1/2. With that, the problem has been solved! I hope this helps you out. Good luck!

5 0

3 years ago

Hugo and Sandy leave a campsite and walk in different directions. After several hours,Hugo has walked 5.6 miles east while Sandy

Alexeev081 [22]

Answer:

8.9 miles.

Step-by-step explanation:

5.6 + 3.3 = 8.9

This should be the answer, however, if this is a coordinate grid question, then it could slope. The answer I have given is not for slope.

4 0

3 years ago

What decimal is equal to 6/25

alukav5142 [94]

6/25 is equal to 0.24 in decimal form

3 0

4 years ago

Read 2 more answers

У = 2х – 6у = х2 – 4х + 2​

У = 2х – 6у = х2 – 4х + 2