Can someone please help :c <3

g You are planning an opinion study and are considering taking an SRS of either 200 or 600 people. Explain how the sampling dist

Katen [24]

Answer:

By the Central Limit Theorem, both would be approximately normal and have the same mean. The difference is in the standard deviation, since as the sample size increases, the standard deviation decreases. So the SRS of 600 would have a smaller standard deviation than the SRS of 200.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sampling distribution of size n of a sample proportion p, the mean is p and the standard deviation is $s = \sqrt{\frac{p(1-p)}{n}}$

Differences between SRS of 200 and of 600

By the Central Limit Theorem, both would be approximately normal and have the same mean. The difference is in the standard deviation, since as the sample size increases, the standard deviation decreases. So the SRS of 600 would have a smaller standard deviation than the SRS of 200.

6 0

3 years ago

The College Board SAT college entrance exam consists of three parts: math, writing and critical reading (The World Almanac 2012)

Wittaler [7]

Answer:

Yes, there is a difference between the population mean for the math scores and the population mean for the writing scores.

Test Statistics = $\frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } }$ follows $t_n_- _1$ .

Step-by-step explanation:

We are provided with the sample data showing the math and writing scores for a sample of twelve students who took the SAT ;

Let A = Math Scores ,B = Writing Scores and D = difference between both

So, $\mu_A$ = Population mean for the math scores

$\mu_B$ = Population mean for the writing scores

Let $\mu_D$ = Difference between the population mean for the math scores and the population mean for the writing scores.

Null Hypothesis, $H_0$ : $\mu_A = \mu_B$ or $\mu_D$ = 0

Alternate Hypothesis, $H_1$ : $\mu_A \neq \mu_B$ or $\mu_D \neq$ 0

Hence, Test Statistics used here will be;

$\frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } }$ follows $t_n_- _1$ where, Dbar = Bbar - Abar

$s_D$ = $\sqrt{\frac{\sum D_i^{2}-n*(Dbar)^{2}}{n-1}}$

n = 12

Student Math scores (A) Writing scores (B) D = B - A

1 540 474 -66

2 432 380 -52

3 528 463 -65

4 574 612 38

5 448 420 -28

6 502 526 24

7 480 430 -50

8 499 459 -40

9 610 615 5

10 572 541 -31

11 390 335 -55

12 593 613 20

Now Dbar = Bbar - Abar = 489 - 514 = -25

Bbar = $\frac{\sum B_i}{n}$ = $\frac{474+380+463+612+420+526+430+459+615+541+335+613}{12}$ = 489

Abar = $\frac{\sum A_i}{n}$ = $\frac{540+432+528+574+448+502+480+499+610+572+390+593}{12}$ = 514

∑ $D_i^{2}$ = 22600 and $s_D$ = $\sqrt{\frac{\sum D_i^{2}-n*(Dbar)^{2}}{n-1}}$ = $\sqrt{\frac{22600 - 12*(-25)^{2} }{12-1} }$ = 37.05

So, Test statistics = $\frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } }$ follows $t_n_- _1$

= $\frac{-25 - 0}{\frac{37.05}{\sqrt{12} } }$ follows $t_1_1$ = -2.34

Now at 5% level of significance our t table is giving critical values of -2.201 and 2.201 for two tail test. Since our test statistics doesn't fall between these two values as it is less than -2.201 so we have sufficient evidence to reject null hypothesis as our test statistics fall in the rejection region .

Therefore, we conclude that there is a difference between the population mean for the math scores and the population mean for the writing scores.

8 0

3 years ago

How do u solve 1×-2y=4 -1×+10y=8

Molodets [167]

Answer: x = -8 ; y = -6

Step-by-step explanation:

1*x-2*y=4

1*x = 4 + 2*y

x = 4 + 2*y

Now you replace the value of x on the following equation:

-1*x+10*y=8

-1*(4 + 2*y) = 8

-4 - 2*y = 8

-2*y = 8+4

-2*y = 12

y = -12/2

y = -6

You replace the value of y in the previous equation:

x = 4 + 2*y

x = 4 + 2*(-6)

x = 4 - 12

x = -8

6 0

3 years ago

1. The sum of a two-digits number is 13. The tens digit is 8 less than twice the units digit. What is the number?

alexgriva [62]

Answer:

The number is 67

Step-by-step explanation:

Equations

Let's consider the number 83. The tens digit is 8 and the unit digit is 3. Note the tens digit's addition to the number is 80, and the unit's addition is 3. This means the tens digit adds 10 times its value, that is, 83 = 8*10 + 3.

Now, let's consider the number ab, where a is the tens digit, and b is the unit digit. It follows that

Number=10*a+b

The question gives us two conditions:

1) The sum of a two-digits number is 13.

2) The tens digit is 8 less than twice the units digit.

The first condition can be expressed as:

a + b = 13 [1]

And the second condition can be written as:

a = 2b-8 [2]

Replacing [2] into [1], we have:

2b-8 + b = 13

Operating:

3b = 13 + 8

3b = 21

Solving for b:

b = 21 / 3 = 7

Substituting into [2]:

a = 2*(7) - 8 = 6

Thus, the number is 67

3 0

3 years ago

What type of quadrilateral has to the vertices A(3,6), B(3,3), C(6,3), and D(6,6)

prisoha [69]

a square as the distance between the lengths and widths are 3

8 0

4 years ago